#1
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àŢ¡¡ÓÅѧ
$2^n\left|\,\right. 2553^{24}-2553^{16}-2553^8+1$ áÅéÇ n ·ÕèÁÒ¡·ÕèÊØ´ÁÕ¤èÒà·èÒäËÃè
ªèÇ hint ËÃ×ÍáÊ´§ÇÔ¸Õ·Ó´éǤѺ »Å.¼ÁᡵÑÇ»ÃСͺä»ààÅéÇààµè仵èÍäÁèà»ç¹ |
#2
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ÍéÒ§ÍÔ§:
¾Ô¨ÒÃ³Ò $2553^n+1$ ËÒôéÇ 4 äÁèŧµÑÇáµè 2 ËÒÃŧµÑÇ
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Always BE yourself
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#3
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¼ÁäÁèÃÙé¶Ù¡äËÁªèǵÃǨ·Õ¤ÃѺ
ãËé $A=2553$ $ 2553^{24}-2553^{16}-2553^8+1=(A-1)(A+1)(A^2+1)(A^4+1)(A^8+1)^2$ $~~~~~~~~~~~~~~~~~~~~~~=(2552)(2554)(2553^2+1)(2553^4+1)(2553^8+1)^2$ $~~~~~~~~~~~~~~~~~~~~~~=2^{3+1+1+1+1+1}\cdot (blah blah)$ $n=8$ãªèäËÁ¤ÃѺ 08 ¡ØÁÀҾѹ¸ì 2011 20:30 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ BLACK-Dragon |
#4
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@#3
¶Ù¡áÅéǤÃѺ áµèäÍé $2553^2+1$ ÍФÃѺʧÊÑÂÇèÒ¾ÔÁµ¡à»ÅèÒ¤ÃѺ ==''
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Always BE yourself
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#5
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#4
¢Íº¤Ø³·ÕèªèǵÃǨ¤ÃѺ ¼Á¤Ô´ÇèÒ¹èÒ¨Ðà»ç¹â¨·Âì¢Í§ ʾ°.Ãͺ 2 »Õ·ÕèáÅéÇËÃ×Íà»ÅèÒ¤ÃѺ $(x^2−5x+6)^3+(x^2−9x+20)=8(x^2−7x+13)^2$ á¡éÊÁ¡ÒÃÂѧä§ËÃͤÃѺ |
#6
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ÍéÒ§ÍÔ§:
»Å. áµè¡ÃШÒÂàÍÒ¡çä´é¹Ð¤ÃѺ
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à˹×Í¿éÒÂѧÁÕ¿éÒáµèà˹×Í¢éÒµéͧäÁèÁÕã¤Ã »Õ¡¢Õé¼×駢ͧ»ÅÍÁ§Ñé¹ÊԹР...âÅ¡¹ÕéâË´ÃéÒ¨ÃÔ§æ ÁѹãËé¤ÇÒÁÊØ¢¡ÑºàÃÒ áÅéÇÊØ´·éÒ Áѹ¡çàÍҤ׹ä»... |
#7
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ÍéÒ§ÍÔ§:
⨷Âì¨ÃÔ§Áѹà»ç¹¡ÓÅѧÊÒÁËÁ´äÁèãªèàËÃͤÃѺ =='' ¶éÒà»ç¹¡ÓÅѧÊÒÁ¹Ð¤ÃѺ¡çàÊ¡µÑÇá»ÃãËÁèà»ç¹ $(x^2−5x+6)=A$ $(x^2−9x+20)=B$ àÃÒ¨Ðä´éÇèÒ $2(x^2−7x+13)= A+B$
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Always BE yourself
08 ¡ØÁÀҾѹ¸ì 2011 20:49 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ÃÒªÒÊÁ¡Òà |
#8
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ÍéÒ§ÍÔ§:
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#9
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¤Ô´ä´é n=13 ¤Ñº ¢Íº¤Ø³ÁÒ¡¤Ñº
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#10
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ÍéÒ§ÍÔ§:
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#11
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Åͧ¢é͹Õé´ÙÁÑé¤ÃѺ ¹èÒʹء
¨§ËҨӹǹ¹Ñº $n$ ·Õè¹éÍ·ÕèÊØ´«Öè§ $2549|n^{2545}-2541$
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¢ÇéÒ§ÁØ¢àÊÕèÂÇ æ ãÊè¡Ñ¹¹èÒ¨ÐÁѹáÎÐ
08 ¡ØÁÀҾѹ¸ì 2011 21:19 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 2 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Influenza_Mathematics |
#12
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ÍéÒ§ÍÔ§:
2549 à»ç¹¨Ó¹Ç¹à©¾ÒÐ(¨Ò¡¡ÒõÃǨÊͺâ´Âà¤Ã×èͧ¤Ô´àÅ¢) $n^{2548}\equiv 1 \pmod{2549}$ àÁ×èÍ $(n,2549)=1$ ¨Ò¡·ÕèÇèÒ $2549|n^{2545}-2541$ ¨Ðä´éÇèÒ $2549|n^{2548}-2541n^3$ áÊ´§ÇèÒ $2549|1-2541n^3$ $-2541n^3 \equiv 8n^3 \pmod{2549} $ $n^{2548}+8n^3 \equiv 8n^3+1 \pmod{2549}$ $2n+1 = 2549$ $n=1274$ äÁèÃÙéÇèÒÁÕ¹éÍ¡ÇèÒ¹ÕéäËÁ¹Ð¤ÃѺ
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no pain no gain |
#13
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Vouloir c'est pouvoir |
#14
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$8n^3+1=(2n+1)(4n^2-2n+1)$
¶éÒ $4n^2-2n+1=2549$ ¨ÐäÁèÁդӵͺà»ç¹¨Ó¹Ç¹àµçÁÍèФÃѺ áµè»ÑËÒ¤×ÍäÁèá¹èã¨ÇèÒ¹éÍ·ÕèÊØ´ËÃ×Íà»ÅèÒ
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no pain no gain |
#15
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#14
¡çÅͧáÊ´§ÇèÒ $2549\nmid(4n^2-2n+1)$ ÊÔ¤ÃѺ |
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