#1
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àŢ¡¡ÓÅѧ
¤ÓµÍºã¹ËÅѡ˹èÇ¢ͧ 7 ¡¡ÓÅѧ 6841 à»ç¹à·èÒääÃѺªèǺ͡ÇԸդԴ˹èÍÂ
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#2
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¶éÒÁÕ¤ÇÒÁÃÙéàÃ×èͧ ÊÁÀÒ¤ (Conguence) ¨Ð§èÒ¤ÃѺàÃÔèÁ¨Ò¡
$7^{2}\equiv -1 mod 10$ $(7^{2})^{3420}=(-1)^{3420}\equiv 1 mod 10$ $7^{6841}=(7^{2})^{3420}\cdot 7\equiv 7 mod 10$ ´Ñ§¹Ñé¹ àÅ¢ã¹ËÅѡ˹èǤ×Í 7 ¤ÃѺ
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#3
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ÊѧࡵØàÅ¢ËÅѡ˹èǤÃѺ
$7^1àÅ¢ËÅѡ˹èǤ×Í7$ $7^2àÅ¢ËÅѡ˹èǤ×Í9$ $7^3àÅ¢ËÅѡ˹èǤ×Í3$ $7^4àÅ¢ËÅѡ˹èǤ×Í1$ $7^5àÅ¢ËÅѡ˹èǤ×Í7$ à»ç¹ 7 9 3 1 7 9 3 1...ä»àÃ×èÍÂæ¤ÃѺ Áѹ¨ÐǹàÅ¢ÊÕèµÑǹÕéä»àÃ×èÍÂæ¤ÃѺ(àÅ¢ 7 9 3 1 ) à¾ÃÒЩйÑé¹àÃÒ¨Ö§ àÍÒ 4 ä» ËÒà 6841 ä´é 1710 àÈÉ 1¤ÃѺ ËÁÒ¤ÇÒÁÇèÒàÃÒÊÒÁÒö¹ÑºàÅ¢ÊÕèµÑǹÕé ǹä»Ç¹ÁÒä´é 1710 Ãͺ ¡ÑºàÈÉÍÕ¡ 1µÑÇ ¤×ÍàÅ¢ 7 ¤ÃѺ µÍºàÅ¢ 7 ¤ÃѺ 20 ¡Ã¡®Ò¤Á 2008 18:45 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Ne[S]zA |
#4
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ËÅѡ˹èÇÂÁѹ¨Ðǹä»àÕÃ×èÍÂæÍèÐ
àªè¹$2^1 = 2$ ËÅѡ˹èǤ×Í 2 $2^2 = 4$ ËÅѡ˹èǤ×Í 4 $2^3 = 8 $ËÅѡ˹èǤ×Í 8 $2^4 = 16 $ËÅѡ˹èǤ×Í 6 ǹµèÍ $2^5 = 32 $ËÅѡ˹èǤ×Í 2 $2^6 = 64 $ËÅѡ˹èǤ×Í 4 $2^7 = 128 $ËÅѡ˹èǤ×Í 8 $2^8 = 256 $ËÅѡ˹èǤ×Í 6ǹµèÍ $2^9 = 512 $ËÅѡ˹èǤ×Í2 $2^{10} = 1024 $ËÅѡ˹èǤ×Í 4 $2^{11} = 2048 $ËÅѡ˹èǤ×Í 8 $2^{12}= 4096$ ËÅѡ˹èǤ×Í 6ǹµèÍ......
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10 µØÅÒ¤Á 2008 20:46 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 7 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¤usÑ¡¤³Ôm à˵ؼÅ: latex |
#5
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ÍèФèÐ ¤Ô´àËÁ×͹¤Ø³ Ne[S]zA áÅéÇÁÕÇÔ¸ÕÍ×è¹äËÁ¤Ð·Õèà¢éÒ㨧èÒÂæáÅéÇ¡çàÃçÇ¡ÇèÒÍèФèÐ ÁÕäËÁ?
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#6
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äÁè¹èÒ¨ÐÁÕáÅéǹФÃѺ¼ÁÇèÒ ÍÔÍÔ(áµèÍÒ¨ÁÕÇÔ¸Õá»Å¡æ ¤³ÔµÈÒʵÃì¤Ô´ä´éËÅÒÂÇÔ¸Õ¤ÃѺ)
21 ¡Ã¡®Ò¤Á 2008 22:10 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Ne[S]zA |
#7
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ÇÔ¸Õá¹Ð¹Ó
¨ÓËÅѡ˹èÇ¢ͧ¼ÅÅѾ¸ìäÇé
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#8
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ÍéÒ§ÍÔ§:
$7^2$ ŧ·éÒ´éÇ 9 $7^3$ ŧ·éÒ´éÇ 3 $7^4$ ŧ·éÒ´éÇ 1 $7^5$ ŧ·éÒ´éÇ 7 . . ... $\therefore$ àŢⴴã¹ËÅѡ˹èǨÐǹ«éÓ·Ø¡æ 4 µÑÇ $7^{6841}$ ¨Ö§Å§·éÒ´éÇ 7 |
#9
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ÇéÒÇ
à¢éÒ㨢Öé¹àÂÍÐàà*0*
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Imagination is more important than knowledge.
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#10
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Åͧ´Ùá¹Ç¤Ô´àÃ×èͧàÅ¢ËÅѡ˹èÇ¢ͧàŢ¡¡ÓÅѧã¹ÅÔ§¤ì¢éÒ§ÅèÒ§´Ù¹Ð¤ÃѺ
http://www.mathcenter.net/forum/show...7848#post27848 ¾ºÇèÒ (6841)/4 ¨ÐÁÕàÈÉà·èҡѺ (41)/4 <-- ¤Ô´à©¾ÒÐ 2 ËÅÑ¡·éÒ (à¹×èͧ¨Ò¡ 6800 ËÒôéÇ 4 ŧµÑÇ, à¾ÃÒÐ 100/4 = 25) áÅÐ 41/4 = 10 àÈÉ 1 ´Ñ§¹Ñé¹ $7^{6841}$ ÁÕàÅ¢ËÅѡ˹èÇÂàËÁ×͹¡Ñº $7^1$ «Ö觡ç¤×Í 7 ¹Ñè¹àͧ |
#11
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Áѹà»ç¹¤ÇÒÁÃÙé¢Í§ªèǧªÑé¹ä˹¤ÑºªèǺ͡˹èÍÂ(àËç¹ààÅéÇäÁèÃÙéàÃ×èͧàÅÂ)
19 ÊÔ§ËÒ¤Á 2008 19:46 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¡Ãza_ba_yo |
#12
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àŪèǧªÑé¹áÅéÇÍèФÃѺ à¾ÃÒÐà»ç¹à¹×èÍËҢͧ ».µÃÕ ËÃ×ÍäÁè¡ç¢Í§ ÊÍǹ. »ÃÐÁÒ³¹Õé áµè¼ÁàËç¹à´ç¡ËÅÒ¤¹
·Óâ´ÂãªéàÃ×èͧ¹Õéä´é ¡çà»ç¹ÍÕ¡ÇÔ¸Õ·Õèà¨ë§ÁÒ¡æ¤ÃѺ à»ç¹¡ÒûÃÐÂØ¡µìãªé¤Í¹¡Ùà͹µì ã¹àÃ×èͧËÒàÈÉ ·ÕèºÒ§¤ÃÑ駡ÒÃËÒ¸ÃÃÁ´ÒÁѹÂØè§ÂÒ¡«Ñº«é͹ ã¤Ãµéͧ¡Òý֡⨷Âì´éÇÂËÅÒÂæá¹Ç¤Ô´¡ç¤§¨ÐÁÕ»ÃÐ⪹ìäÁèÁÒ¡¡ç¹éÍ ÊèǹÇèÒ¨Ðä»ËÒä´é·Õèä˹à¹Õ ã¹àÇ»ºÍÃì´¹Õé¡çÁÕàÂÍФÃѺ Åͧ¤é¹ËÒ ¾ÔÁ¾ì¤ÓÇèÒ conguence ËÃ×Í ¤Í¹¡Ùà͹«ì ´Ù¹Ð¤ÃѺ
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#13
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ÍÂÒ¡ÃØé¨Ñ§¤ÃѺÁѹàÍÒä»ãªèã¹àÃ×èͧ¡ÒäԴÍÐäÃä´éºéÒ§¤ÃѺ¨ÐÅͧàÍÒãªèºéÒ§
à¼×èÍÁѹ¨Ð¤Ô´äÇ¡èÒà´ÔÁ àËÍæ ¡ç¾Íà¢éÒã¨ÍйФÃѺ ã¨ÁÒ¡æàÅ à»ç¹ÍÐä÷ÕèÊØ´ÂÍ¡ÁÑ¡ÁÑ¡ ÍÔÍÔ |
#14
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äÁèÃÙéÊÔ¤ÃѺ àÂÍÐÁÒ¡àÅ (¡ÒÃËÒàÈÉ ¼Åà©Å·Õèà»ç¹¨Ó¹Ç¹àµçÁ ¡ÒÃËÒ¢é͢ѴáÂé§ ÏÅÏ)
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#15
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µÍº 7 ¤ÃѺâ´Â¡ÒùÓ4ä»ËÒÃáÅéǹÓàÈÉ·Õèä´éÁÒà»ç¹àŢ¡¡ÓÅѧ
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