1. ³]¦¹¤»¦ì¼ÆABCDEF¬°¤T¦ì¼Æaxb¤§¥¤è AB=16®É¡Aaxb¦ôp¥i¯à¬°401~410¡A¦ý410¤£¦X ¦P²z¡A·íAB=25,36,49,64,81®É¡Ax§¡À³¬°0 ¦]¦¹ì¤T¦ì¼Æ¤§¤Q¦ì¼Æ¦r¥²¬°o ¦p¦¹¥i³]¦¹¤T¦ì¼Æ¬°100a+b¡Aa=4~9¡Ab=4~9 (100a+b)^2=a^2*10000+2ab*100+b^2¡A¦¹®É¤¤¶¡¤G¦ì¼Æ¦rAB=2ab 2ab=k^2¡Aa,b¦Ü¤Ö¨ä¤@¬°2ªº¿¼Æ¡A¦]¦¹(a,b)=(4,8),(8,4) ¬G¦¹¤»¦ì¼Æ¬°408^2©Î804^2¡A¥ç§Y166464¡A646416
2. ³]n^2+n+7=k^2¡A«h(n+1/2)^2+27/4=k^2 ¨âÃä¦P¼4¥i±o4k^2-(2n+1)^2=27 ³]l2kl=A¡Al2n+1l=B¡A A > B > 0 ¡@(A+B)(A-B)=27*1=9*3¡A¨ä¸Ñ¬°(A,B)=(14,13),(6,3) ¡@B=13©Î3¡A2n+1=-13,13,-3,3¡A¦]¦¹n=-7,6,-2,1 ¬G©Ò¦³mªº¿n=-7*-2*1*6=84
3. ³]¦ÛµM¼Æ¬°A, X^2=A+94¡AY^2=A-19¡AlXl > lYl ¡@¡@¨â¦¡¬Û´î±oX^2-Y^2=113 ¡@¡@(lXl+lYl)(lXl-lYl)=113*1¸Ñ±o(lXl¡AlYl)=(57¡A56) ¥N¤J±oA=3155
4. ³]¦¹°¸¼Æ¬°¤G¦ì¼Æ10A+B¤§¥¤è¡AA=4,6,8¡AB=2,4,6,8 (10A+B)^2=A^2*100+2AB*10+B^2¡A¨ä¤¤2AB¬°°¸¼Æ¡A³]¨äÓ¦ì¼Æ¦r¬°k¡Ak¥²¬°°¸¼Æ B^2=4,16,36,64¡A·íB^2=16,36®É¡A²£¥Í¤§¤Q¦ì¼Æ¦r¬°k+1¡Ak+3§¡¬°©_¼Æ¡A¤£¦X ¦]¦¹B=2©Î8¡A¦ÓA=4,6,8¡A¬G¤G¦ì¼Æ10A+B¥i¯à¬°42,48,62,68,82,88 42,62¥¤è¬°1***,3***¡A¤£¦X¡A¦AÀˬd48,82,88§¡¤£¦X¡A¬G¦¹°¸¼Æ¬°68^2=4624
µù:©êºp! ³oÃD¤§«e¸Ñ¹L,»~¬°¤G¦ì¼Æ°¸¼Æ¤§¥¤è,¦]¦¹±o¥t¸Ñ92^2,¦ý²{¥Ñ°¸¼Æ½X²Õ¦¨ªº¤G¦ì¼Æ«h¸ÑÃD¸û¥ý«e²³æ¦h¤F. |