| 丢番图方程(a-1)x~2+(91a+9)=4a~n |
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| 引用本文： | 李志刚,袁平之.丢番图方程(a-1)x~2+(91a+9)=4a~n[J].数学学报,2010,53(1):37-44. |
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| 作者姓名： | 李志刚 袁平之 |
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| 作者单位： | 湖南科技大学数学与计算科学学院;华南师范大学数学科学学院; |
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| 基金项目： | 国家自然科学基金资助项目(10571180,10771058); 广东省自然科学基金资助项目(8151027501000114) |
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| 摘 要： | 本文将证明:若整数a≥2,且a≠5,方程(a-1)x~2+(91a+9)=4a~n无满足2(?)n的正整数解(x,n);若a=5,则此方程满足2(?)n的正整数解(x,n)=(3,3).
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| 关 键 词： | 广义Ramanujan-Nagell方程 Legendre定理的推广 本原素因子 |
| 收稿时间： | 2008-06-25 |
| 修稿时间： | 2009-03-17 |
On the Diophantine Equations (a-1)x2+(91a+9)=4an |
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| Zhi Gang LI School of Mathematics , Computing Science,Hu\'nan University of Science , Technology,Xiangtan ,P.R.China Ping Zhi YUAN School of Mathematics,South China Normal University,Guangzhou ,P.R.China.On the Diophantine Equations (a-1)x2+(91a+9)=4an[J].Acta Mathematica Sinica,2010,53(1):37-44. |
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| Authors: | Zhi Gang LI School of Mathematics Computing Science Hu\'nan University of Science Technology Xiangtan PRChina Ping Zhi YUAN School of Mathematics South China Normal University Guangzhou PRChina |
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| Institution: | 1. School of Mathematics and Computing Science, Hu'nan University of Science and Technology, Xiangtan 411201, P. R. China;
2. School of Mathematics, South China Normal University, Guangzhou 510631, P. R. China |
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| Abstract: | In this paper,we prove that if a≥2 is an integer and a≠5,the equations (a - 1)x~2 +(91a + 9) = 4a~n have no positive integer solutions(x,n) with 2(?) n;if a = 5, the equation has the only solution(x,n) =(3,3) with 2(?)n. |
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| Keywords: | generalized Ramanujan-Nagell equations extension of Legendre\'s theorem primitive divisors |
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