| 关于丢番图方程(x+1)2+(x+2)2+…+(x+n)2=y2 |
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| 引用本文： | 李树新.关于丢番图方程(x+1)2+(x+2)2+…+(x+n)2=y2[J].广西民族大学学报,2006(Z2):2-9. |
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| 作者姓名： | 李树新 |
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| 作者单位： | 广西民族大学数学与计算机科学学院 广西南宁530006 |
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| 摘 要： | 利用数论方法得到了丢番图(x 1)2 (x 2)2 … (x n)2=y2有正整数解的必要充分条件,证明了当n=25时,无正整数解,当n=49时,仅有正整数解(x,y)=(24,357),当n=121时仅有正整数解(x,y)=(243,3366),同时证明了n=2,11时必有无穷多组正整数解,并给出了无穷多解的通解公式.
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| 关 键 词： | 丢番图方程 正整数解 Lacas猜想 |
| 文章编号： | 1007-0311(2006)ZJ01-0002-08 |
| 修稿时间： | 2006年9月30日 |
About Diophantus Equation (x+1)2 + (x+2)2+ … + (x+n)2 = y2 |
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| LI Shu-xin.About Diophantus Equation (x+1)2 + (x+2)2+ … + (x+n)2 = y2[J].Journal of Guangxi University For Nationalities(Natural Science Edition),2006(Z2):2-9. |
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| Authors: | LI Shu-xin |
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| Abstract: | Utilizing the number theory method to be lost picture equation once,there is essential abundant condition that straight integer solves,have proved that acts as n =At 25 o'clock,there is not positive number that is solved,act as n =Only there are positive numbers that are solved at 49 o' clock,act as n =Only there are positive numbers that are solved at 121 o'clock,meanwhile,proved that acts as n =2,11must have infinite large group's positive numbers solve one o'clock,and provide the infinite general solution formula that solve more. |
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| Keywords: | Diophantus equations positive integer solution Lacas conjecture |
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