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<title>*奇想西卡*</title> 
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	<modified>2010-07-18T22:57:20+08:00</modified> 
<tagline>&lt;p&gt;單車、攝影、象棋、電腦、網路、打屁、聊天。 [排球、文學、漫畫 快要被我作廢掉了 sigh]&lt;/p&gt;
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 <entry> 
 <id>tag:blog.segaa.net,2010-07-18:1181</id>
 <title>[手機] HTC diamond on Android 2.1</title> 
 <link rel="alternate" type="text/html" href="http://blog.segaa.net/blog.php/1/post/1/1181" /> 
  
 <modified>2010-07-18T22:57:20+08:00</modified> 
 <issued>2010-07-18T22:57:20+08:00</issued> 
 <created>2010-07-18T22:57:20+08:00</created> 
 <summary type="text/plain">    HTC diamond 這手機買了快兩年 ,, 刷了不少大大小小的ROM  &amp;nbsp;  最後沉迷在 gpower 威能底下  &amp;nbsp;  不過 gpower 也幾乎不更新了 &amp;nbsp;, &amp;nbsp;&amp;nbsp;  &amp;nbsp; ...</summary> 
 <author> 
  
 <name>segaa</name> 
 <url>http://blog.segaa.net/blog.php/1</url> 
</author> 
<dc:subject>
General 
</dc:subject> 
 <content type="text/html" mode="escaped" xml:lang="zh-tw" xml:base="http://blog.segaa.net/blog.php/1"> 
 &lt;div&gt;&lt;br /&gt;&lt;/div&gt;&lt;div&gt;HTC diamond 這手機買了快兩年 ,, 刷了不少大大小小的ROM&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;最後沉迷在 gpower 威能底下&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;不過 gpower 也幾乎不更新了 &amp;nbsp;, &amp;nbsp;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;最後一個 ROM 畫面&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&lt;img src=&quot;http://images.plurk.com/3313475_3a0ef92277ee1cdd25e40171aa8e679d.jpg&quot; width=&quot;453&quot; height=&quot;604&quot; /&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;基本上完全符合需求了 , &amp;nbsp;可以撥接電話、出門在外可以開 papago 導航 、開個 wifi 上上網看看東西&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;真的沒WIFI也可以開通威寶單日3G上網&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;不過當機不斷也鈍鈍的&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;升級不能、 更新無望 身邊的人也一個一個跳 iphone 跟 android&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;也害我想換手機了&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;去年就看到有人用外掛的android在 dimond上執行&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;但是 wifi 不能 、 gPS不能、相機不能 ,, 所以就放棄了&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;直到最近發現新版的 android 2.1 成熟多了&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;參考 :&amp;nbsp;&lt;a href=&quot;http://www.mobile01.com/topicdetail.php?f=224&amp;amp;t=1525030&amp;amp;last=21001545&quot;&gt;http://www.mobile01.com/topicdetail.php?f=224&amp;amp;t=1525030&amp;amp;last=21001545&lt;/a&gt;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;原始網址&amp;nbsp;&lt;a href=&quot;http://forum.xda-developers.com/showthread.php?t=621498&quot;&gt;http://forum.xda-developers.com/showthread.php?t=621498&lt;/a&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&amp;nbsp;&lt;/div&gt;&lt;div&gt;基本上幾乎完美了，&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;安裝蠻簡單的 , 基本上抓下 cab檔後一直跑就好了&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;不過執行很慢要有耐心 ... &amp;nbsp;一度還以為死當了&lt;/div&gt;&lt;div&gt;&amp;nbsp;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&lt;img src=&quot;http://pic.segaa.net/albums/userpics/10002/20100718/normal_SUMMER_146.jpg&quot; width=&quot;550&quot; height=&quot;308&quot; /&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;用了幾天感覺很順手,&amp;nbsp;market更是方便&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;缺點&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;1. 太耗電 , 使用中幾乎就是燙電力也是直線的消耗 ...&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;2. 有點頓 (雖然習慣了 diamond 跑M2 也是盾阿...)&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;3. 相機還不能用&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;除此以外已經可以完全取代 wm6.1 (or 6.5) , 害我好心動想去敗一隻原生 android 2.2 的來用 &lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;gt;__________ &amp;lt;&amp;quot;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&lt;a href=&quot;http://forum.xda-developers.com/showthread.php?t=711692&quot;&gt;http://forum.xda-developers.com/showthread.php?t=711692&lt;/a&gt;&lt;/div&gt;&lt;div&gt;&lt;span class=&quot;Apple-style-span&quot; style=&quot;font-size: 12px; font-family: verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; color: #111111&quot;&gt;[prj][XDANDROID][2.2][AOSP][18.7.10]RC1 RELEASED&lt;/span&gt;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;android 2.2 也出了 ,, 等成熟一點在裝上去試試看 &amp;nbsp;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;span style=&quot;line-height: 15px; font-family: &#039;Trebuchet MS&#039;, Arial, sans-serif; color: #111111&quot;&gt;&lt;span style=&quot;line-height: 18px; font-size: medium&quot;&gt;&lt;strong style=&quot;border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 18px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;Known Issues&lt;/strong&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;line-height: 15px; font-family: &#039;Trebuchet MS&#039;, Arial, sans-serif; color: #111111&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;span style=&quot;line-height: 15px; font-family: &#039;Trebuchet MS&#039;, Arial, sans-serif; color: #111111&quot;&gt;Many things are still not working properly, and the developers are fully aware of 99% of them.&lt;/span&gt;&lt;span style=&quot;line-height: 15px; font-family: &#039;Trebuchet MS&#039;, Arial, sans-serif; color: #111111&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;ul style=&quot;margin-top: 1em; margin-right: 0px; margin-bottom: 1em; margin-left: 0px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left: 40px; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; list-style-type: disc; list-style-position: initial; list-style-image: initial; display: block; font-family: &#039;Trebuchet MS&#039;, Arial, sans-serif; color: #111111; line-height: 15px; border-width: 0px&quot;&gt;			&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;SDCard - Most SDCards are working, but if you the &#039;waiting for SDCard&#039; message, you should try one of these fixes (and please let us know if it works)&lt;br /&gt;		Fix 1: Format your card with this tool&amp;nbsp;&lt;a id=&quot;link_6&quot; href=&quot;http://www.sdcard.org/consumers/formatter/&quot; target=&quot;_blank&quot;&gt;http://www.sdcard.org/consumers/formatter/&lt;/a&gt;&lt;br /&gt;		Fix 2: Edit your startup.txt file and add these entries to your cmdline:&lt;br /&gt;		&lt;span style=&quot;line-height: 12px; font-size: xx-small&quot;&gt;&lt;em style=&quot;border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 12px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;set cmdline &amp;quot;lcd.density=240 msmts_calib=0x395.0x3c9.0x79.0x77 clock-7x00.a11=500 msmvkeyb_toggle=off pmem.extra=1 gsensor_axis=-2,-1,3&amp;nbsp;&lt;span style=&quot;line-height: 12px; color: red&quot;&gt;&lt;br /&gt;		&lt;strong style=&quot;border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 12px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;msmsdcc_1bit msmsdcc_fmax=14000000 msmsdcc_nopwrsave&lt;/strong&gt;&lt;/span&gt;&amp;quot;&lt;/em&gt;&lt;/span&gt;&lt;br /&gt;		Fix 3: Tell your wife / girlfriend that you are about to make some modifications to her phone... change the ringtone and steal her old Class 2 SD Card to use with Android. She will never discover what you have done, and if she does, you&#039;ll be able to use Android to send texts to your former girlfriends ;-)&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;&lt;span style=&quot;color: #ff0000&quot;&gt;Camera - Not working&lt;/span&gt;&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;GPS - Should be working, but it&#039;s only just been enabled (so could be buggy)&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;Battery Status - Highly problematic for most users (don&#039;t trust the capacity Android tells you, it&#039;s simply up and down a lot, and highly inaccurate)&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;WiFi - Working for most people, suspected to cause slight heat, definitely drains the battery faster than WinMo. Some users have reported freezes when switching WiFi off&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;Audio - Speaker working for most people, microphone can have issues&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;Deep Sleep - Working for most people, but can have issues waking up (sometimes, it will not wake up)&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;GPRS - Working&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;3G - Working for most&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;PIN Code - Not working&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;GSensor - Working (Screen only handles 0 and 270 degrees)&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;Bluetooth - Experimentally working (don&#039;t expect too much, but it&#039;s working for a number of users)&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;OpenGL ES - Not working&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;USB - Supported, but will NOT operate in mass storage mode. You can charge via USB and you can debug, but forget accessing your files by it.&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;Headphone Socket - Semi working (see FAQ for details on how to make it work)&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;Application Errors: It&#039;s very common to see &#039;Application (xxxxxx) is not responding: Force Close or Wait&#039;. Click wait. I do not know the precise reason for this, but from what I can gather, it COULD be related to the slow speed of the SD Card causing the app response times to JUST be a little too slow for Android&#039;s liking, thus causing the message. This seems to happen more after bootup or wakeup when the device is busy doing stuff in the background.&lt;/li&gt;		&lt;li style=&quot;font: normal normal normal 10pt/normal verdana, geneva, lucida, &#039;lucida grande&#039;, arial, helvetica, sans-serif; border-style: initial; border-color: initial; outline-width: 0px; outline-style: initial; outline-color: initial; font-size: 13px; background-image: initial; background-attachment: initial; background-origin: initial; background-clip: initial; background-color: transparent; display: list-item; border-width: 0px; padding: 0px; margin: 0px&quot;&gt;Cannot choose ringtones: This is believed to be caused by the media scanner failing (due to discovering some filenames with none English characters). The best option of all is to use a CLEAN SD Card. But, if you insist on hosting other files on the same SD Card, you MUST make sure they have English character filenames.&lt;/li&gt;&lt;/ul&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt;&lt;div&gt;&amp;nbsp;&lt;/div&gt; 
</content> 
</entry> 
 
 <entry> 
 <id>tag:blog.segaa.net,2005-11-03:25</id>
 <title>[文件] 電子交易安全 期中考 -2</title> 
 <link rel="alternate" type="text/html" href="http://blog.segaa.net/blog.php/1/post/1/25" /> 
  
 <modified>2005-11-03T17:44:02+08:00</modified> 
 <issued>2005-11-03T17:44:02+08:00</issued> 
 <created>2005-11-03T17:44:02+08:00</created> 
 <summary type="text/plain">  之前版本有幾個錯誤先修改了，就重寄一份希望不會打擾到大家 ^^;;    檔案中紅字為修改過部分。      第一題：補上第二個式子的證明 ...</summary> 
 <author> 
  
 <name>segaa</name> 
 <url>http://blog.segaa.net/blog.php/1</url> 
</author> 
<dc:subject>
General 
</dc:subject> 
 <content type="text/html" mode="escaped" xml:lang="zh-tw" xml:base="http://blog.segaa.net/blog.php/1"> 
 &lt;div&gt;&lt;font size=&quot;2&quot;&gt;之前版本有幾個錯誤先修改了，就重寄一份希望不會打擾到大家 ^^;;&lt;/font&gt;&lt;/div&gt;&lt;div&gt;&lt;font size=&quot;2&quot;&gt;檔案中紅字為修改過部分。&lt;/font&gt;&lt;/div&gt;&lt;div&gt;&lt;/div&gt;&lt;div&gt;&lt;font size=&quot;2&quot;&gt;第一題：補上第二個式子的證明&lt;/font&gt;&lt;/div&gt;&lt;div&gt;&lt;font size=&quot;2&quot;&gt;第二題：第二個式子筆記沒抄到不知道有哪為好心的人士幫忙補上 ,,&lt;/font&gt;&lt;/div&gt;&lt;div&gt;&lt;font size=&quot;2&quot;&gt;第五題： Z3 的三個表應該是寫錯了，再mod 3 之下 應該不會有大於三的數 (感謝士軒的提醒)&lt;/font&gt;&lt;/div&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;MARGIN-LEFT: 18pt; TEXT-INDENT: -18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;span&gt;1.&lt;span style=&quot;FONT-FAMILY: &quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;寫出並證明費碼定理&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;Fermat &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;定理&lt;/span&gt; &lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;，當&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; (a,p)=1 (a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;跟&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;p&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;互質&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;a. &lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;p-1&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot;&gt; = 1 mod p&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;證明：在&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;Zp &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;之中&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;、&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;p&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;互質&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;[1*2*3..*(p-1)]modp={(1*a)(&lt;st1 tcsc=&quot;0&quot; numbertype=&quot;1&quot; negative=&quot;False&quot; hasspace=&quot;False&quot; sourcevalue=&quot;2&quot; unitname=&quot;a&quot; /&gt;2a&lt;/st1 /&gt;)(&lt;st1 tcsc=&quot;0&quot; numbertype=&quot;1&quot; negative=&quot;False&quot; hasspace=&quot;False&quot; sourcevalue=&quot;3&quot; unitname=&quot;a&quot; /&gt;3a&lt;/st1 /&gt;)...[a(p-1)]}modp &amp;lt;-&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;同成&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;係數只是重排&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;={a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;(p-1)&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot;&gt;*[1*2*3..*(p-1)]}modp &amp;lt;-&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;右邊將&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;提出成為&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;的&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;p-1&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;次方&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;因為&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;、&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;p&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;互質所以存在反元素將兩邊同乘反元素&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; [1*2*3..*(p-1)]&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;-1&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot;&gt; &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;消掉&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;所以&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; 1modp = a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;(p-1)&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot;&gt;modp -&amp;gt; a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;p-1&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot;&gt; = 1 mod p&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;b. a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;p&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt; = a mod p &lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;證明：假設&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt; (a,p)&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;≠&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;1 &lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;則&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt; a&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;為&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;p&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;的倍數&lt;/span&gt;&lt;span style=&quot;red: &quot;&gt; &lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;並可寫成&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;p&lt;/span&gt;&lt;/sup&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;≠&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;a mod p&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;&lt;span&gt;&lt;/span&gt;&lt;span&gt;&lt;/span&gt;a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;p&lt;/span&gt;&lt;/sup&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;≠&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;a mod p &lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;&lt;span&gt;&lt;/span&gt;a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;p&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt; –a &lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;≠&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt; (a-a) mod p&lt;span&gt; &lt;/span&gt;(&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;兩邊同減&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;a)&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;&lt;span&gt;&lt;/span&gt;a(a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;p-1&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt; –1) &lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;≠&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt; 0 mod p&lt;span&gt; &lt;/span&gt;(&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;左邊將&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;a&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;提出&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;)&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;&lt;span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;&lt;span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;∵&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;a(a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;p-1&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt; –1) &lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;≠&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt; 0 mod p &lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;&lt;span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;&lt;span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;∴&lt;span lang=&quot;EN-US&quot;&gt; p&lt;/span&gt;不整除&lt;span lang=&quot;EN-US&quot;&gt; a &lt;/span&gt;且&lt;span lang=&quot;EN-US&quot;&gt;p&lt;/span&gt;不整除&lt;span lang=&quot;EN-US&quot;&gt; (&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;p-1&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt; –1&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;) &lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 12pt&quot;&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;與假設不符合所以得證&lt;span lang=&quot;EN-US&quot;&gt;&lt;span&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;p&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;=a mod p&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;&lt;span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;MARGIN-LEFT: 18pt; TEXT-INDENT: -18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;span&gt;2.&lt;span style=&quot;FONT-FAMILY: &quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;寫出並證明尤拉定理&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;尤拉定理&lt;/span&gt; &lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;，當&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; (a,p)=1 (a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;跟&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;p&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;互質&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;a.&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt; a&lt;sup&gt;Φ(n)&lt;/sup&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;＝&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;1 mod n&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;[X1*X2*X3..XΦ(n)]mod n =[(X1modn)(X2modn)(X3modn)…[XΦ(n)]modn] modn&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;([(X1modn)(X2modn)(X3modn)…[XΦ(n)]modn] modn &lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;同乘&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;a&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;等於係數重排&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;)&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;= [aX1modn aX2modn aX3modn …. [aXΦ(n)]modn ] modn &lt;span style=&quot;red: &quot;&gt;(&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;右邊係數同乘&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;a)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;=a&lt;sup&gt;Φ(n)&lt;/sup&gt;&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; [X1*X2*X3..XΦ(n)]modn&lt;span&gt; &lt;/span&gt;&lt;span style=&quot;red: &quot;&gt;(&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;右邊將&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;a&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;提出&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;) &lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;&lt;o /&gt;&lt;/span&gt;&lt;/sup&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;1 mod n= a&lt;sup&gt;Φ(n)&lt;span style=&quot;red: &quot;&gt; &lt;span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/sup&gt;&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;(&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;左右同乘反元素&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;[X1*X2*X3..XΦ(n)]&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;-1&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;)&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;&lt;o /&gt;&lt;/span&gt;&lt;/sup&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;得證：&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;a&lt;sup&gt;Φ(n)&lt;/sup&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;＝&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;1 mod n&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;b.&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt; &lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;當&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt; (a,n)&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;≠&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;1&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;　且&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;(a&amp;lt;n) &lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;，&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;a&lt;sup&gt;Φ(n&lt;/sup&gt;&lt;/span&gt;&lt;sup&gt;&lt;span style=&quot;FONT-SIZE: 14pt; COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;＋&lt;/span&gt;&lt;/sup&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;1)&lt;/span&gt;&lt;/sup&gt;&lt;span style=&quot;FONT-SIZE: 14pt; COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;＝&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt; COLOR: red&quot;&gt;a mod n&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;MARGIN-LEFT: 18pt; TEXT-INDENT: -18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;span&gt;3.&lt;span style=&quot;FONT-FAMILY: &quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;寫出並證明&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;RSA&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;所用的基本定理&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;RAS&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;基本定理：&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;代表一個訊&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;息，&lt;span lang=&quot;EN-US&quot;&gt;n=p*q &lt;/span&gt;， &lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n)+1&lt;/sup&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;＝&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;m mod n&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;a.&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;當&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; (m,n) = 1 &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;根據尤拉定理&lt;/span&gt; &lt;span lang=&quot;EN-US&quot;&gt;a&lt;sup&gt;Φ(n)&lt;/sup&gt; &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;＝&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; 1 mod n &lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n)+1&lt;/sup&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;＝&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;m mod n(&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;兩邊同乘&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;後得證&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; )&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;b.&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;當&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; (m,n)&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;≠&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;span&gt; &lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;所以　&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;b&lt;st1 tcsc=&quot;0&quot; numbertype=&quot;1&quot; negative=&quot;True&quot; hasspace=&quot;True&quot; sourcevalue=&quot;1&quot; unitname=&quot;m&quot; /&gt;-1 m&lt;/st1 /&gt; = C1p&lt;span&gt; &lt;/span&gt;b&lt;st1 tcsc=&quot;0&quot; numbertype=&quot;1&quot; negative=&quot;True&quot; hasspace=&quot;True&quot; sourcevalue=&quot;2&quot; unitname=&quot;m&quot; /&gt;-2 m&lt;/st1 /&gt; = C2q&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span&gt;&lt;/span&gt;b&lt;st1 tcsc=&quot;0&quot; numbertype=&quot;1&quot; negative=&quot;True&quot; hasspace=&quot;True&quot; sourcevalue=&quot;1&quot; unitname=&quot;m&quot; /&gt;-1 m&lt;/st1 /&gt; = C1 * p , (m , q) = 1 &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;根據尤拉定理可寫為　&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(q)&lt;/sup&gt; &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;＝&lt;/span&gt; &lt;span lang=&quot;EN-US&quot;&gt;1 mod q&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;[m&lt;sup&gt;Φ(q)&lt;/sup&gt;]&lt;sup&gt; Φ(p)&lt;/sup&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;＝&lt;/span&gt; &lt;span lang=&quot;EN-US&quot;&gt;1&lt;sup&gt;Φ(p)&lt;/sup&gt;mod q ( &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;兩邊同乘&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;Φ(p) &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;次方&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n)&lt;/sup&gt; = 1 mod q&lt;span&gt; &lt;/span&gt;(&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;因為&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; n =p*q&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;，&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;的任何次方還是&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;1 )&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n)&lt;/sup&gt; = 1+kq&lt;span&gt; &lt;/span&gt;(&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;存在一整數&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;k&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;，&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;1modq = 1+kq)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n+1)&lt;/sup&gt; =m + kqm (&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;兩邊同乘&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;m) &lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n+1)&lt;/sup&gt; = m + kqC1p&lt;span&gt; &lt;/span&gt;(m =C1*p&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;代入&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n+1)&lt;/sup&gt; = m + kC1n&lt;span&gt; &lt;/span&gt;(&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;其中&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; n=p*q&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;代入&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n+1)&lt;/sup&gt; = m mod n&lt;span&gt; &lt;/span&gt;(m+kC1n&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;等於&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; m mod n)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span&gt;&lt;/span&gt;b&lt;st1 tcsc=&quot;0&quot; numbertype=&quot;1&quot; negative=&quot;True&quot; hasspace=&quot;True&quot; sourcevalue=&quot;2&quot; unitname=&quot;m&quot; /&gt;-2 m&lt;/st1 /&gt; = C2*q &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;同&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; b-1 &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;可證&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; m&lt;sup&gt;Φ(n+1)&lt;/sup&gt; = m mod n&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;MARGIN-LEFT: 18pt; TEXT-INDENT: -18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;span&gt;4.&lt;span style=&quot;FONT-FAMILY: &quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;證明&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt; (a+b) mod n = [(a mod n) + (b mod n)] mod n&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;假設&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; (a mod n)= Ra (b mod n) = Rb , &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;則&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; a = Ra + j n ;&lt;span&gt; &lt;/span&gt;b = Rb + kn &lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;(a+b) mod n = [(Ra+jn )+(Rb+kn) ]mod n&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span&gt;&lt;/span&gt;= [Ra+Rb+ (j+k)n ] mod n&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span&gt;&lt;/span&gt;=(Ra+Rb) mod n &amp;lt;- &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;根據假設&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; (a mod n)= Ra (b mod n) = Rb&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;帶入&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span&gt;&lt;/span&gt;= [(a mod n )+ (b mod n )] mod n&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;MARGIN-LEFT: 18pt; TEXT-INDENT: -18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;span&gt;5.&lt;span style=&quot;FONT-FAMILY: &quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;何謂一個體&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;, &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;做&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt; Z&lt;sub&gt;3&lt;/sub&gt; &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;的三個表&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;體：&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;除了&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;0&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;之外，有兩個交換環&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;(&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;加法和乘法&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;)&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;，加法和乘分具分配律，並有不具有&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;0&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;的真因子，除&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;0&lt;/span&gt;&lt;span style=&quot;COLOR: red; FONT-FAMILY: 新細明體&quot;&gt;之外皆有反元素&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;table class=&quot;MsoTableGrid&quot; style=&quot;BORDER-COLLAPSE: collapse; medium: &quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;1&quot;&gt;&lt;tbody&gt;&lt;tr style=&quot;20: &quot;&gt;&lt;td style=&quot;PADDING-RIGHT: 5.4pt; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; WIDTH: 37.5pt; PADDING-TOP: 0cm; HEIGHT: 20.5pt; medium: &quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;加法&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: medium none; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: medium none; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: &quot;&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: medium none; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: &quot;&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: medium none; HEIGHT: 20.1pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.1pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.1pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.1pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;0&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: &quot;&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: medium none; HEIGHT: 20.95pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.95pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.95pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;0&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.95pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;1&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;table class=&quot;MsoTableGrid&quot; style=&quot;BORDER-COLLAPSE: collapse; medium: &quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;1&quot;&gt;&lt;tbody&gt;&lt;tr style=&quot;20: &quot;&gt;&lt;td style=&quot;PADDING-RIGHT: 5.4pt; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; WIDTH: 37.5pt; PADDING-TOP: 0cm; HEIGHT: 20.5pt; medium: &quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;乘法&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: medium none; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: medium none; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: &quot;&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: medium none; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: &quot;&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: medium none; HEIGHT: 20.1pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.1pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.1pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.1pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: &quot;&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: medium none; HEIGHT: 20.95pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.95pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.95pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.95pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;red: &quot;&gt;1&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;table class=&quot;MsoTableGrid&quot; style=&quot;BORDER-COLLAPSE: collapse; medium: &quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;1&quot;&gt;&lt;tbody&gt;&lt;tr style=&quot;20: &quot;&gt;&lt;td style=&quot;BORDER-RIGHT: medium none; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;W&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: medium none; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;-w&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;w&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;-1&lt;/span&gt;&lt;/sup&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: &quot;&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: 1pt solid; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: &quot;&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: 1pt solid; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.1pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.1pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.1pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: &quot;&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: 1pt solid; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.95pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.95pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: medium none; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: medium none; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: 1pt solid; HEIGHT: 20.95pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;MARGIN-LEFT: 18pt; TEXT-INDENT: -18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;span&gt;6.&lt;span style=&quot;FONT-FAMILY: &quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;若&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt; Z=k&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;．&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;Φ(n)+q &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;則&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt; a&lt;sup&gt;z&lt;/sup&gt; = ? mod n&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;a&lt;sup&gt;z&lt;/sup&gt; =a &lt;sup&gt;k&lt;/sup&gt;&lt;/span&gt;&lt;sup&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;．&lt;/span&gt;&lt;/sup&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;Φ(n)+q&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt; = [a&lt;sup&gt;Φ(n)&lt;/sup&gt;]&lt;sup&gt;k&lt;/sup&gt; * a&lt;sup&gt;q&lt;/sup&gt;&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;span&gt;&lt;/span&gt;= {[(a&lt;sup&gt;Φ(n)&lt;/sup&gt;)&lt;sup&gt;k&lt;/sup&gt; modn ][a&lt;sup&gt;q&lt;/sup&gt;modn]}modn (&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;根據尤拉&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt&quot;&gt; &lt;span lang=&quot;EN-US&quot;&gt;a&lt;sup&gt;Φ(n)&lt;/sup&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;＝&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;1modn )&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;span&gt;&lt;/span&gt;= {(1modn)(a&lt;sup&gt;q&lt;/sup&gt;modn)}modn&lt;span&gt; &lt;/span&gt;&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;span&gt;&lt;/span&gt;=a&lt;sup&gt;q&lt;/sup&gt; modn &lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;MARGIN-LEFT: 18pt; TEXT-INDENT: -18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;span&gt;7.&lt;span style=&quot;FONT-FAMILY: &quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;說明&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt&quot;&gt; &lt;span lang=&quot;EN-US&quot;&gt;discrete logarithm problem&lt;o /&gt;&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;離散對數依照方程式：&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;span&gt; &lt;/span&gt;y=g&lt;sup&gt;x&lt;/sup&gt; mod p&lt;span&gt; &lt;/span&gt;&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;給定&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;g x p &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;可以很快算出&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt; y &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;，但是只給&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt; y g p &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;則很難算出&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt; x&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體&quot;&gt;的值。&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;o /&gt;&lt;/o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;MARGIN-LEFT: 18pt; TEXT-INDENT: -18pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt;&lt;span&gt;8.&lt;span style=&quot;FONT-FAMILY: &quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;用&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt; Euclid algorithm &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體&quot;&gt;求&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt&quot;&gt; GCD(86,32)&lt;o /&gt;&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;GCD(86,32)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;86=2*32+22 GCD(32,22)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;32=1*22+10 GCD(22,10)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;22=2*10+2 GCD(10,2)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;10=2*5+0&lt;span&gt; &lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;得&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; GCD(86,32)=2 &lt;/span&gt;&lt;/p&gt; 
</content> 
</entry> 
 
 <entry> 
 <id>tag:blog.segaa.net,2005-11-03:24</id>
 <title>[文件] 電子交易安全期中考</title> 
 <link rel="alternate" type="text/html" href="http://blog.segaa.net/blog.php/1/post/1/24" /> 
  
 <modified>2005-11-03T05:55:00+08:00</modified> 
 <issued>2005-11-03T05:55:00+08:00</issued> 
 <created>2005-11-03T05:55:00+08:00</created> 
 <summary type="text/plain">   1   、   2    題       不確定是否完整，    就是第二個部份的證明不知道要不要寫，    如果需要就要再補上去， ...</summary> 
 <author> 
  
 <name>segaa</name> 
 <url>http://blog.segaa.net/blog.php/1</url> 
</author> 
<dc:subject>
General 
</dc:subject> 
 <content type="text/html" mode="escaped" xml:lang="zh-tw" xml:base="http://blog.segaa.net/blog.php/1"> 
 &lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 16pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;font face=&quot;Times New Roman&quot;&gt;1&lt;/font&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 16pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &#039;Times New Roman&#039;; mso-hansi-font-family: &#039;Times New Roman&#039;&quot;&gt;、&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 16pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;font face=&quot;Times New Roman&quot;&gt;2 &lt;/font&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 16pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &#039;Times New Roman&#039;; mso-hansi-font-family: &#039;Times New Roman&#039;&quot;&gt;題&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 16pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;font face=&quot;Times New Roman&quot;&gt; &lt;/font&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 16pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &#039;Times New Roman&#039;; mso-hansi-font-family: &#039;Times New Roman&#039;&quot;&gt;不確定是否完整，&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-SIZE: 16pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &#039;Times New Roman&#039;; mso-hansi-font-family: &#039;Times New Roman&#039;&quot;&gt;就是第二個部份的證明不知道要不要寫，&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-SIZE: 16pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &#039;Times New Roman&#039;; mso-hansi-font-family: &#039;Times New Roman&#039;&quot;&gt;如果需要就要再補上去，&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-SIZE: 16pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &#039;Times New Roman&#039;; mso-hansi-font-family: &#039;Times New Roman&#039;&quot;&gt;不確定是否有打錯或是筆記操錯的地方&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 16pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &#039;Times New Roman&#039;; mso-hansi-font-family: &#039;Times New Roman&#039;&quot;&gt;有錯請指正，thanks&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: -18pt; 0cm: ; mso-list: l0 level1 lfo1; tab-stops: list 18.0pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: &quot;&gt;&lt;span style=&quot;mso-list: Ignore&quot;&gt;1.&lt;span&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;寫出並證明費碼定理&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;Fermat &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;定理&lt;/span&gt; &lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;，當&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; (a,p)=1 (a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;跟&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;p&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;互質&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;p-1&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot;&gt; = 1 mod p&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;證明：在&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;Zp &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;之中&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;、&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;p&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;互質&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;[1*2*3..*(p-1)]modp={(1*a)(&lt;chmetcnv tcsc=&quot;0&quot; numbertype=&quot;1&quot; negative=&quot;False&quot; hasspace=&quot;False&quot; sourcevalue=&quot;2&quot; unitname=&quot;a&quot; /&gt;2a&lt;/chmetcnv /&gt;)(&lt;chmetcnv tcsc=&quot;0&quot; numbertype=&quot;1&quot; negative=&quot;False&quot; hasspace=&quot;False&quot; sourcevalue=&quot;3&quot; unitname=&quot;a&quot; /&gt;3a&lt;/chmetcnv /&gt;)...[a(p-1)]}modp &amp;lt;-&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;同成&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;係數只是重排&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt;&lt;/span&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt;&lt;/span&gt;={a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;(p-1)&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot;&gt;*[1*2*3..*(p-1)]}modp &amp;lt;-&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;右邊將&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;提出成為&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;的&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;p-1&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;次方&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;因為&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;、&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;p&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;互質所以存在反元素將兩邊同乘反元素&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; [1*2*3..*(p-1)]&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;-1&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot;&gt; &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;消掉&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;所以&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; 1modp = a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;(p-1)&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot;&gt;modp -&amp;gt; a&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;p-1&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot;&gt; = 1 mod p&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: -18pt; 0cm: ; mso-list: l0 level1 lfo1; tab-stops: list 18.0pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: &quot;&gt;&lt;span style=&quot;mso-list: Ignore&quot;&gt;2.&lt;span&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;寫出並證明尤拉定理&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;尤拉定理&lt;/span&gt; &lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;，當&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; (a,p)=1 (a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;跟&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;p&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;互質&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;a&lt;sup&gt;Φ(n)&lt;/sup&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;＝&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;1 mod n&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;[X1*X2*X3..XΦ(n)]mod n =[(X1modn)(X2modn)(X3modn)…[XΦ(n)]modn] modn&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;[(X1modn)(X2modn)(X3modn)…[XΦ(n)]modn] modn &amp;lt;=&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;同乘&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;等於係數重排&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;= [aX1modn aX2modn aX3modn …. [aXΦ(n)]modn ] modn &amp;lt;- &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;將&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;a&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;提出&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;=a&lt;sup&gt;Φ(n)&lt;/sup&gt;&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; [X1*X2*X3..XΦ(n)]modn&lt;span style=&quot;mso-spacerun: yes&quot;&gt; &lt;/span&gt;&amp;lt;= &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;同乘反元素&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;[X1*X2*X3..XΦ(n)]&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;-1&lt;/span&gt;&lt;/sup&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;1 mod n= a&lt;sup&gt;Φ(n)&lt;/sup&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: -18pt; 0cm: ; mso-list: l0 level1 lfo1; tab-stops: list 18.0pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: &quot;&gt;&lt;span style=&quot;mso-list: Ignore&quot;&gt;3.&lt;span&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;寫出並證明&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;RSA&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;所用的基本定理&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;RAS&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;基本定理：&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;代表一個訊&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體&quot;&gt;息，&lt;span lang=&quot;EN-US&quot;&gt;n=p*q &lt;/span&gt;， &lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n)+1&lt;/sup&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;＝&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;m mod n&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;a.&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;當&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; (m,n) = 1 &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;根據尤拉定理&lt;/span&gt; &lt;span lang=&quot;EN-US&quot;&gt;a&lt;sup&gt;Φ(n)&lt;/sup&gt; &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;＝&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; 1 mod n &lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n)+1&lt;/sup&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;＝&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;m mod n(&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;兩邊同乘&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;後得證&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; )&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;b.&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;當&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; (m,n)&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;≠&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;span style=&quot;mso-spacerun: yes&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;所以　&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;b&lt;chmetcnv tcsc=&quot;0&quot; numbertype=&quot;1&quot; negative=&quot;True&quot; hasspace=&quot;True&quot; sourcevalue=&quot;1&quot; unitname=&quot;m&quot; /&gt;-1 m&lt;/chmetcnv /&gt; = C1p&lt;span style=&quot;mso-spacerun: yes&quot;&gt; &lt;/span&gt;b&lt;chmetcnv tcsc=&quot;0&quot; numbertype=&quot;1&quot; negative=&quot;True&quot; hasspace=&quot;True&quot; sourcevalue=&quot;2&quot; unitname=&quot;m&quot; /&gt;-2 m&lt;/chmetcnv /&gt; = C2q&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt;&lt;/span&gt;b&lt;chmetcnv tcsc=&quot;0&quot; numbertype=&quot;1&quot; negative=&quot;True&quot; hasspace=&quot;True&quot; sourcevalue=&quot;1&quot; unitname=&quot;m&quot; /&gt;-1 m&lt;/chmetcnv /&gt; = C1 * p , (m , q) = 1 &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;根據尤拉定理可寫為　&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt; 0cm: ; mso-char-indent-count: 1.5&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(q)&lt;/sup&gt; &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;＝&lt;/span&gt; &lt;span lang=&quot;EN-US&quot;&gt;1 mod q&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt; 0cm: ; mso-char-indent-count: 1.5&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;[m&lt;sup&gt;Φ(q)&lt;/sup&gt;]&lt;sup&gt; Φ(p)&lt;/sup&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;＝&lt;/span&gt; &lt;span lang=&quot;EN-US&quot;&gt;1&lt;sup&gt;Φ(p)&lt;/sup&gt;mod q ( &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;兩邊同乘&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;Φ(p) &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;次方&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt; 0cm: ; mso-char-indent-count: 1.5&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n)&lt;/sup&gt; = 1 mod q&lt;span style=&quot;mso-spacerun: yes&quot;&gt; &lt;/span&gt;(&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;因為&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; n =p*q&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;，&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;的任何次方還是&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;1 )&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt; 0cm: ; mso-char-indent-count: 1.5&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n)&lt;/sup&gt; = 1+kq&lt;span style=&quot;mso-spacerun: yes&quot;&gt; &lt;/span&gt;(&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;存在一整數&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;k&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;，&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;1modq = 1+kq)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt; 0cm: ; mso-char-indent-count: 1.5&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n+1)&lt;/sup&gt; =m + kqm (&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;兩邊同乘&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;m) &lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt; 0cm: ; mso-char-indent-count: 1.5&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n+1)&lt;/sup&gt; = m + kqC1p&lt;span style=&quot;mso-spacerun: yes&quot;&gt; &lt;/span&gt;(m =C1*p&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;代入&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt; 0cm: ; mso-char-indent-count: 1.5&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n+1)&lt;/sup&gt; = m + kC1n&lt;span style=&quot;mso-spacerun: yes&quot;&gt; &lt;/span&gt;(&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;其中&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; n=p*q&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;代入&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt;)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: 18pt; 0cm: ; mso-char-indent-count: 1.5&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;m&lt;sup&gt;Φ(n+1)&lt;/sup&gt; = m mod n&lt;span style=&quot;mso-spacerun: yes&quot;&gt; &lt;/span&gt;(m+kC1n&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;等於&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; m mod n)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt;&lt;/span&gt;b&lt;chmetcnv tcsc=&quot;0&quot; numbertype=&quot;1&quot; negative=&quot;True&quot; hasspace=&quot;True&quot; sourcevalue=&quot;2&quot; unitname=&quot;m&quot; /&gt;-2 m&lt;/chmetcnv /&gt; = C2*q &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;同&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; b-1 &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;可證&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; m&lt;sup&gt;Φ(n+1)&lt;/sup&gt; = m mod n&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: -18pt; 0cm: ; mso-list: l0 level1 lfo1; tab-stops: list 18.0pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: &quot;&gt;&lt;span style=&quot;mso-list: Ignore&quot;&gt;4.&lt;span&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;證明&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt; (a+b) mod n = [(a mod n) + (b mod n)] mod n&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;假設&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; (a mod n)= Ra (b mod n) = Rb , &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;則&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; a = Ra + j n ;&lt;span style=&quot;mso-spacerun: yes&quot;&gt; &lt;/span&gt;b = Rb + kn &lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;(a+b) mod n = [(Ra+jn )+(Rb+kn) ]mod n&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt;&lt;/span&gt;= [Ra+Rb+ (j+k)n ] mod n&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt;&lt;/span&gt;=(Ra+Rb) mod n &amp;lt;- &lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;根據假設&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; (a mod n)= Ra (b mod n) = Rb&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;帶入&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt;&lt;/span&gt;= [(a mod n )+ (b mod n )] mod n&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: -18pt; 0cm: ; mso-list: l0 level1 lfo1; tab-stops: list 18.0pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: &quot;&gt;&lt;span style=&quot;mso-list: Ignore&quot;&gt;5.&lt;span&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;何謂一個體&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;, &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;做&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt; Z&lt;sub&gt;3&lt;/sub&gt; &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;的三個表&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;體：俱有兩個交換環，並有不具有&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;的真因子，除&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;0&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;之外皆有反元素&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;table class=&quot;MsoTableGrid&quot; style=&quot;BORDER-RIGHT: medium none; BORDER-TOP: medium none; BORDER-LEFT: medium none; BORDER-BOTTOM: medium none; BORDER-COLLAPSE: collapse; mso-border-alt: solid windowtext .5pt; mso-yfti-tbllook: 480; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;1&quot;&gt;&lt;tbody&gt;&lt;tr style=&quot;20: ; mso-yfti-irow: 0; mso-yfti-firstrow: yes&quot;&gt;&lt;td style=&quot;BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: #f0f0f0; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;加法&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: ; mso-yfti-irow: 1&quot;&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: #f0f0f0; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-right-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: ; mso-yfti-irow: 2&quot;&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: #f0f0f0; HEIGHT: 20.1pt; BACKGROUND-COLOR: transparent; mso-border-right-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.1pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.1pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.1pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;3&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: ; mso-yfti-irow: 3; mso-yfti-lastrow: yes&quot;&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: #f0f0f0; HEIGHT: 20.95pt; BACKGROUND-COLOR: transparent; mso-border-right-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.95pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.95pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;3&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.95pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;4&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;table class=&quot;MsoTableGrid&quot; style=&quot;BORDER-RIGHT: medium none; BORDER-TOP: medium none; BORDER-LEFT: medium none; BORDER-BOTTOM: medium none; BORDER-COLLAPSE: collapse; mso-border-alt: solid windowtext .5pt; mso-yfti-tbllook: 480; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;1&quot;&gt;&lt;tbody&gt;&lt;tr style=&quot;20: ; mso-yfti-irow: 0; mso-yfti-firstrow: yes&quot;&gt;&lt;td style=&quot;BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: #f0f0f0; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;乘法&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: ; mso-yfti-irow: 1&quot;&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: #f0f0f0; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-right-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: ; mso-yfti-irow: 2&quot;&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: #f0f0f0; HEIGHT: 20.1pt; BACKGROUND-COLOR: transparent; mso-border-right-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.1pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.1pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.1pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: ; mso-yfti-irow: 3; mso-yfti-lastrow: yes&quot;&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: #f0f0f0; HEIGHT: 20.95pt; BACKGROUND-COLOR: transparent; mso-border-right-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.95pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.95pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.95pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;4&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;table class=&quot;MsoTableGrid&quot; style=&quot;BORDER-RIGHT: medium none; BORDER-TOP: medium none; BORDER-LEFT: medium none; BORDER-BOTTOM: medium none; BORDER-COLLAPSE: collapse; mso-border-alt: solid windowtext .5pt; mso-yfti-tbllook: 480; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext&quot; cellspacing=&quot;0&quot; cellpadding=&quot;0&quot; border=&quot;1&quot;&gt;&lt;tbody&gt;&lt;tr style=&quot;20: ; mso-yfti-irow: 0; mso-yfti-firstrow: yes&quot;&gt;&lt;td style=&quot;BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;w&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: #f0f0f0; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;-w&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;w&lt;/span&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;-1&lt;/span&gt;&lt;/sup&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: ; mso-yfti-irow: 1&quot;&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 1pt solid; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.5pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;0&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: ; mso-yfti-irow: 2&quot;&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 1pt solid; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.1pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.1pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.1pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr style=&quot;20: ; mso-yfti-irow: 3; mso-yfti-lastrow: yes&quot;&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: windowtext 1pt solid; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.95pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.95pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;1&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;td style=&quot;BORDER-RIGHT: windowtext 1pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #f0f0f0; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #f0f0f0; WIDTH: 37.5pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 1pt solid; HEIGHT: 20.95pt; BACKGROUND-COLOR: transparent; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt&quot; valign=&quot;top&quot; width=&quot;50&quot;&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;2&lt;/span&gt;&lt;/p&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/tbody&gt;&lt;/table&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: -18pt; 0cm: ; mso-list: l0 level1 lfo1; tab-stops: list 18.0pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: &quot;&gt;&lt;span style=&quot;mso-list: Ignore&quot;&gt;6.&lt;span&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;若&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt; Z=k&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;．&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;Φ(n)+q &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;則&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt; a&lt;sup&gt;z&lt;/sup&gt; = ? mod n&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;a&lt;sup&gt;z&lt;/sup&gt; =a &lt;sup&gt;k&lt;/sup&gt;&lt;/span&gt;&lt;sup&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;．&lt;/span&gt;&lt;/sup&gt;&lt;sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;Φ(n)+q&lt;/span&gt;&lt;/sup&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt; = [a&lt;sup&gt;Φ(n)&lt;/sup&gt;]&lt;sup&gt;k&lt;/sup&gt; * a&lt;sup&gt;q&lt;/sup&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt;&lt;/span&gt;= {[(a&lt;sup&gt;Φ(n)&lt;/sup&gt;)&lt;sup&gt;k&lt;/sup&gt; modn ][a&lt;sup&gt;q&lt;/sup&gt;modn]}modn (&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;根據尤拉&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt&quot;&gt; &lt;span lang=&quot;EN-US&quot;&gt;a&lt;sup&gt;Φ(n)&lt;/sup&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;＝&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;1modn )&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt;&lt;/span&gt;= {(1modn)(a&lt;sup&gt;q&lt;/sup&gt;modn)}modn&lt;span style=&quot;mso-spacerun: yes&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt;&lt;/span&gt;=a^&lt;sup&gt;q&lt;/sup&gt; modn &lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: -18pt; 0cm: ; mso-list: l0 level1 lfo1; tab-stops: list 18.0pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: &quot;&gt;&lt;span style=&quot;mso-list: Ignore&quot;&gt;7.&lt;span&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;說明&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt; discrete logarithm problem&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;0cm: ; tab-stops: 250.5pt&quot;&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;離散對數依照方程式：&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;span style=&quot;mso-spacerun: yes&quot;&gt; &lt;/span&gt;y=g&lt;sup&gt;x&lt;/sup&gt; mod p&lt;span style=&quot;mso-tab-count: 1&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;0cm: ; tab-stops: 250.5pt&quot;&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;給定&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;g x p &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;可以很快算出&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt; y &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;，但是只給&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt; y g p &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;則很難算出&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt; x&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 14pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;的值。&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 14pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot; style=&quot;TEXT-INDENT: -18pt; 0cm: ; mso-list: l0 level1 lfo1; tab-stops: list 18.0pt&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: &quot;&gt;&lt;span style=&quot;mso-list: Ignore&quot;&gt;8.&lt;span&gt; &lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;用&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt; Euclid algorithm &lt;/span&gt;&lt;span style=&quot;FONT-SIZE: 18pt; FONT-FAMILY: 新細明體; mso-bidi-font-size: 12.0pt; mso-ascii-font-family: &quot;&gt;求&lt;/span&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt; GCD(86,32)&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;GCD(86,32)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;86=2*32+22 GCD(32,22)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;32=1*22+10 GCD(22,10)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;22=2*10+2 GCD(10,2)&lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;10=2*5+0&lt;span style=&quot;mso-spacerun: yes&quot;&gt; &lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;FONT-FAMILY: 新細明體; mso-ascii-font-family: &quot;&gt;得&lt;/span&gt;&lt;span lang=&quot;EN-US&quot;&gt; GCD(86,32)=2 &lt;/span&gt;&lt;/p&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 18pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p class=&quot;MsoNormal&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;FONT-SIZE: 16pt; mso-bidi-font-size: 12.0pt&quot;&gt;&lt;/span&gt;&lt;/p&gt;&lt;p /&gt;&lt;p /&gt;&lt;p /&gt;&lt;p /&gt;&lt;p /&gt;&lt;p /&gt;&lt;p /&gt;&lt;p /&gt;&lt;p /&gt;&lt;p /&gt;&lt;p /&gt;&lt;p /&gt;&lt;p /&gt;&lt;p /&gt; 
</content> 
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 <entry> 
 <id>tag:blog.segaa.net,2005-09-22:1</id>
 <title>Congratulations!</title> 
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 <modified>2005-09-22T14:46:10+08:00</modified> 
 <issued>2005-09-22T14:46:10+08:00</issued> 
 <created>2005-09-22T14:46:10+08:00</created> 
 <summary type="text/plain">If you can read this post, it means that the registration process was successful and that you can start blogging</summary> 
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General 
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 If you can read this post, it means that the registration process was successful and that you can start blogging 
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