µo¥¬ªÌ | ¤º®e¦C | celine.yang06 Quite a regular
µù¥U¤é: 2007-08-28 µoªí¼Æ: 44
| | 2007-09-28 23:16 | | bubupin Home away from home
µù¥U¤é: 2007-03-13 µoªí¼Æ: 353
| Re: ¬°¤°»ò¥¤è¼Æ³o»ò¯«©_¡H | | (a^2+b^2+c^2+d^2)(e^2+f^2+g^2+h^2) =(ae+bf+cg+dh)^2+(af-be+ch-dg)^2+(ag-bh-ce+df)^2+(ah+bg-cf-de)^2
±N¥ô·N¥¿¾ã¼ÆA´£¥X³Ì¤j¥¤è¼Æ»P¨ä¥L½è¦]¼Æ¤§¼¿n ¥OA=x^2*p*q*r...... Y¹ï¥ô·N½è¼Æp,q,r....ùÚ¯àªí¥Ü¦¨ p=a1^2+b1^2+c1^2+d1^2¡Aq=a2^2+b2^2+c2^2+d2^2¡Ar=a3^2+b3^2+c3^2+d3^2........
«hp*q=(a1^2+b1^2+c1^2+d1^2)(a2^2+b2^2+c2^2+d2^2)=a^2+b^2+c^2+d^2
p*q*r=(a^2+b^2+c^2+d^2)(a3^2+b3^2+c3^2+d3^2)=a'^2+b'^2+c'^2+d'^2
¦p¦¹A=x^2*p*q*r......¥iªí¥Ü¬°¥|Ó¥¤è¼Æ¤§©M ¤wª¾2=1^2+1^2+0^2+0^2 ¦]¦¹¥unÃÒ©ú¥ô¤@©_½è¼Æ¥iªí¥Ü¬°¥|Ó¥¤è¼Æ¤§©M§Y¥i(¥|Ó¥¤è¼Æ¬°¥¿¾ã¼Æ©Î0)
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| 2007-10-02 13:13 | | bubupin Home away from home
µù¥U¤é: 2007-03-13 µoªí¼Æ: 353
| Re: ¬°¤°»ò¥¤è¼Æ³o»ò¯«©_¡H | | ¦pªG§A¬O°ê¤¤¤p¥Í¡A«Øij±z°µ¥H¤UÀËÅç§Y¥i¡D Àˬd¥ô·N¥¿¾ã¼Æ¡Aµo²{¨ä¤¤¬Y¨Ç¼ÆµLªkªí¥Ü¦¨¤TÓ¥¤è¼Æ©M 7,15,23,31,39,47,55,63,.................. 28,60,92,124,156,188,220,.............. 112,240,368,496,624,752,880,........... ³o¨Ç¼Æ¥i¥HÂk¯Ç¦¨4^m(8k+7)ªº«¬¦¡ ´«¥y¸Ü»¡¡A4^m(8k)¡A4^m(8k+1)¡A.....4^m(8k+5)¡A4^m(8k+6) ¬O¥i¥Hªí¥Ü¦¨¤TÓ¥¤è¼Æ©M ¦Ó4^m(8k+7)=4^m(8k+6)+4^m=a^2+b^2+c^2+(2^m)^2 ¦]¦¹¥ô·N¥¿¾ã¼Æ¡A¬Ò¥iªí¥Ü¦¨¥|Ó¥¤è¼Æ©M
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| 2007-10-02 22:33 | | bubupin Home away from home
µù¥U¤é: 2007-03-13 µoªí¼Æ: 353
| Re: ¬°¤°»ò¥¤è¼Æ³o»ò¯«©_¡H | | 1. ¥ô¦ó¥¤è¼Æ¬Ò§e4x©Î4x+1«¬ºA¡A¬G¹ï¥ô¦ó§e4x+3«¬¦¡ªº¼Æ¡A¥²µLªkªí¥Ü¦¨¨â¥¤è¼Æ©M¡A±N½è¼Æp¤À¬°4k+1©M4k+3¨âºØ¡A¹ï¥¿¾ã¼Æa¡Aa=1~p-1¡A¨Da^2°£¥Hpªº¾l¼Æ¡A¹ï4k+1«¬½è¼Æ¥i²£¥Í2kºØ¾l¼Æ¡A¦Ó4k+3«¬½è¼Æ¥i²£¥Í2k+1ºØ¾l¼Æ ¨Ò¦p¡G 4k+1«¬17:1,4,9,16,8,2,15,13,|13,15,2,8,16,9,4,1¡A¦³8ºØ¾l¼Æ¡A¥i²£¥Í¥|²Õ¾l¼Æ¬Û¥[µ¥©ó17 4k+3«¬(k¬°°¸¼Æ)11:1,4,9,5,3,|3,5,9,4,1¡A²£¥Í¤ºØ¾l¼Æ¡AY±N¨ä¼2¦A°£¥H11¡A¥i§ä¨ì¥t5Ó¥i¯à¾l¼Æ 4k+3«¬(k¬°©_¼Æ)23:1,4,9,16,2,13,3,18,12,8,6|...¡A²£¥Í11Ó¾l¼Æ¡A¥ô¨ú¨âÓ¬Û¥[°£¥H11,¥i§ä¨ì¥t11Ó¥i¯à¾l¼Æ¡D 2. ¹ï4k+1«¬½è¼Æp¡A¥i§ä¨ì2k²Õ§e²{a^2+b^2=mp ¨Ò¦p¡G3^2+5^2=2*17¡A6^2+7^2=5*17 ¹ï4k+3½è¼Æp¡A¥i§ä¨ìa^2+b^2+c^2=mp¡Aµø¦Pa^2+b^2+c^2+d^2=mp 1^2+4^2+4^2=3*11¡A2^2+4^2+7^2=3*23 3. ±µ¤U¨Ó¡A§ÚÌ´N4k+1«¬½è¼Æ´M§äa^2+b^2=p¡A§Y¨Dm¤§³Ì¤pÈ1¡A¥Hp=29¬°¨Ò (1)11^2+13^2¬O29ªº10¿¡A§Ú̱N11©M13¤À§O°£¥H10,±o¨ì¤@²Õ¾l¼Æ¬°(1,3) §Q¥Î(a^2+b^2)(c^2+d^2)=(ac+bd)^2+(ad-bc)^2 ¹ïa^2+b^2=mp¦Ó¨¥¡A(ac+bd)¡A(ad-bc)¥²¬°mªº¿¼Æ ±N(11^2+13^2)(1^2+3^2)§ï¼g¦¨=(11*1+13*3)^2+(11*3-13*1)^2=50^2+20^2¡Aµ¥¦¡¨âÃä¦U°£¥H100¡A±o¨ì29=5^2+2^2
(2)¦A°µ¤@¦¸½m²ß¡A³o¦¸¡A·í¾l¼Æ¤j©ó³Q°£¼Æmªº¤@¥b®É¡A§Ṳ́޶it¾lªºÆ[©À 8^2+9^2=5*29¡A(8,9)°£¥H5,±o¨ì¾l¼Æ(3,4)¡A±N(3,4)§ï¦¨(-2,-1)¡A¥H(8,9),(-2,-1)¨Ó¾Þ§@¥i±o|(8*-2+9*-1)|/5=5¡A(8*-1-9*-2)/5=2¡A¦p¦¹¥ç¥i±o¨ì5^2+2^2=29
(3) ¥i¥H¥Î¥ô¤@a^2+b^2=mp±À¥X¨ä¾l¦U²Õ²Å¦Xa^2+b^2=mpªº²Õ¦X ¨Ò¦p¡G§Q¥Î4^2+11^2=137¨D¥X1+x^2=137kªº¥¿¾ã¼Æ¸Ñ §Q¥Ît¾lÆ[©À¡A(4,11)==(4,126)==(2,63)==(2,74)==(1,37) ¥i¥H¨D±o1^2+37^2=137*10 4. ´N4k+3«¬½è¼Æ´M§äa^2+b^2+c^2+d^2=p¡A§Y¨Dm¤§³Ì¤pÈ1¡A¥Hp=23¬°¨Ò¡A2^2+4^2+7^2=3*23 §Q¥Î(a^2+b^2+c^2+d^2)(e^2+f^2+g^2+h^2)=(ae+bf+cg+dh)^2+(af-be+ch-dg)^2+(ag-bh-ce+df)^2+(ah+bg-cf-de)^2 (2^2+4^2+7^2+0^2)(-1^2+1^2+1^2+0^2) =(-2+4+7+0)^2+(2+4+0-0)^2+(2-0+7+0)^2+(0+4-7-0)^2 69*3=9^2+6^2+9^2+3^2 ¦P°£9±o23=3^2+2^2+3^2+1^2 ************************************************************ ¥Ñ¤W¥iª¾¡A4k+1«¬ªº½è¼Æp¡A¥iªí¥Ü¦¨¨âÓ¥¤è¼Æ©M ¦P²z¡A4k+3«¬ªº½è¼Æp¡A¥iªí¥Ü¦¨¥|Ó¥¤è¼Æ©M¡A¬G¹ï¥ô¦ó½è¼Æ¦Ó¨¥¡A§¡¥iªí¥Ü¦¨¥|Ó¥¤è¼Æ©M
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| 2007-10-08 13:27 | | celine.yang06 Quite a regular
µù¥U¤é: 2007-08-28 µoªí¼Æ: 44
| Re: ¬°¤°»ò¥¤è¼Æ³o»ò¯«©_¡H | | bubupin¨û¨û¡G ÁÂÁ±zªº«ü¾É¡A§Æ±æ¬°¤F¸Ñµª§Úªº°ÝÃD¡A¤£·|®ö¶O±z¤Ó¦h®É¶¡¡A³oӸѵª¯uªº§â§ÚÀ~¤@¸õ©O¡I¤§©Ò¥H·|´£¥X³oÓ°ÝÃD¡A¬O¦]¬°§Ú¨ìÂå°|¬Ý¶E¡Aµ¥Ô®É¶¡¹ê¦b¤Ó¤[¤F¡A§Ú´N¥Î¬Ý¶E¸¹½Xª±°_©î¼Æ¹CÀ¸¨Ó¤F¡A¥un¬Ý¶E¿O¸¹¤@Âà´«¡A¥X²{¤@Ó·s¼Æ¦r¡A§Ú°¨¤W¦b¸£®ü¤¤·j´M¬ÛÃöªº¼Æ¦r¥[¥H²Õ¦X¡Aª±µÛª±µÛ¡A´N§ä¥X¤F³o¼Ëªºª±ªk¡A¦ý¬O¤£ª¾¹D¬°¤°»ò·|³o¼Ë¡H¬Ý¤F±zªº¸Ñµª¡Aµo²{¾Ç°Ý¤£¤p©O¡I©Î³§Úªºµ{«×¤Ó®t¤F¡A§Ú²{¦bÁÙ¦b§V¤O«ä¦Ò²z¸Ñ¤¤¡A¦ý¬OÁÙ¬O«D±`ÁÂÁ±z¡I |
| 2007-10-10 20:35 | | bubupin Home away from home
µù¥U¤é: 2007-03-13 µoªí¼Æ: 353
| Re: ¬°¤°»ò¥¤è¼Æ³o»ò¯«©_¡H | | ¡@¡@À³¸Ó¬O§Ú¦V§AÁÂÁ¤~¹ï¡D§Ú¤Þ¥Î³o¤@ÃDÅý§ÚŪ¤p¤»ªº¨à¤l¥h¸Ñ¡A±o¨ìªº¦¬Ã¬¤Q¤ÀÄ_¶Q¡A·í§Ú̱o¨ìªì¨Bªº¦¨ªG®É¡A©~µMµoı¡A¤j¾Ç¤@¦~¯Å°ò¦¼Æ½×½Òµ{¡A·í¤¤©Ò«ü¥Xªº¤º®e«ÂI¡A²[»§ÚÌ©Ò«ä¦Òªº¦UÓ°ÝÃD¡A·íµM¡A¬ã¨s§A³o¤@ÃD¡A§¹¥þ¯¥Íªº¼Æ½×½Òµ{¡A¬Û«H«Ä¤l¥H«á¦³¾÷·|¾Ç¨ì¡A¨ä¹ê¤w¬O¼ô±xªºªF¦è¡D¦ý¦pªG¤£¬O¦]¬°§A³o¤@ÃD¡A·Q·Q¬Ý¡A½Ö·|¥h¸I³o¨Ç°ªF¦è©O¡H§Y¨Ï²{¦b¡An§Ú¥h¶R³oÃþ®ÑÀR¤U¤ß¨Ó¬Ý¤W¤G¤Q¤ÀÄÁ³£«Ü§xÃø¡D¦ý¬O¡A¸Ü¤S»¡¦^¨Ó¡A¤@Ó¤j¾Ç¥Í¡A¦pªG¤§«e¨S¦³¥h±µÄ²¨ì³o¨ÇªF¦è¡A·í¥L¤@¶}©l¾Ç®É¡A¤@©w·|ªá¤@¬q®É¶¡¤~¯à§ì¦í«ÂI¨ÃÅé·|¥X¨ä¤¤ªº¼Ö½ì¡D¦Ó§Ú¤]¬Û«H¡A¦³¨Ç¤Hµ¥¨ì²¦·~«á¡A¥i¯à¤]·d¤£²M·¡¨ì©³¾Ç¨ì¤F¤°»ò¡D ¡@¡@³o¤@ÃD¨ä¹ê¨S¦³¨º»ò½ÆÂø¡A¥u¬O¬°¤FÅý«Ä¤l¥h¾Ç¨ì¦³¥Îªº¬ã¨s¹Lµ{¡A¦P®É¤Þµo¿³½ì¡A¤~·|µ¹¥L¹Á¸Õ¦UÓ¤è¦Vªº«ä¦Ò¡D¥Lªá¥Îªº®É¶¡·¥¤Ö¡A¦ý¹ê»Ú¤W±o¨ìªº³£¬O¦³¥Îªºª¾ÃÑ»P¸gÅç¡D¥H¤Uªº¤èªk¥i¥H´£¨Ñ§A°µ¬°°Ñ¦Ò¡D ¡@¡@¥H½è¼Æ17Á|¨Ò¨Ó»¡¡A§A¥i¥H¸Õ¸Õ¬Ý¥H¤Uªº°µªk¡A³o¼Ë´N®e©ö¦h¤F¡G
1.1~8¦U¼Æªº¥¤è°£©ó17ªº¾l¼Æ¬Ò¤£¬Û¦P 2.±q{1,2,3,4,5,6,.......16}¤¤¨ú¥X8ӼơA¦A±q8Ó¼Æ·í¤¤¥ô¨ú¨â¼Æ¬Û¥[(¥]¬A¦Û¤v¥[¦Û¤v)«á°£¥H17¡A«h¥²¥i±o¥X¨ä¾lªº8ӼơD ¡@¡@¨ä¹ê§A³o¹DÃD¥un¯à°÷ÃÒ©ú¥H¤W¨âÂI¹ï¥ô¦ó½è¼Æ³£¦¨¥ß§Y¥i¡D¦ÓÃÒ©úªº¤èªk¨Ã¤£Ãø¡A§A¤]¤£¥²µ¹§Ú¸Ñµª¡A¥un©ñ¦b¤ßùØ¡A¦³ªÅ¦h·Q·Q´N¥i¥H¤F¡D
¡@¡@§A¬OÓÁo©úªº¤p«Ä¡AÀ´±o§â´¤¹s¸Hªº®É¶¡¥h«ä¦Ò¡A§Úªº«Ä¤l¤]¹³§A¤@¼Ë³ßÅw·Q³o¨Ç¦³ªº¨Sªº¡A¦A¤@¦¸ÁÂÁ§A¡AÅý§Ú̪º¥Í¬¡§ó¥[¥R¹ê¡D
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| 2007-10-10 21:55 | |
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