| Diophantine方程nx~2+2~m=y~n(英文) |
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| 引用本文： | 吴华明.Diophantine方程nx~2+2~m=y~n(英文)[J].数学进展,2011(3). |
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| 作者姓名： | 吴华明 |
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| 作者单位： | 湛江师范学院数学与计算科学学院; |
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| 基金项目： | Supported by NSFC(No.10971184) |
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| 摘 要： | 设n是大于3的奇数.本文运用Y.Bilu,G.Hanrot和P.M.Voutier关于Lehmer数本原素因子存在性的新近结果,证明了方程nx~2+2~m=y~n没有适合gcd(x,y)=1且m为奇数的正整数解(x,y,m).
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| 关 键 词： | 指数Diophantine方程 Lehmer数 本原素因子 |
The Diophantine Equation nx~2+2~m=y~n |
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| WU Huaming.The Diophantine Equation nx~2+2~m=y~n[J].Advances in Mathematics,2011(3). |
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| Authors: | WU Huaming |
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| Institution: | WU Huaming (School of Mathematics and Computational,Zhanjiang Normal College,Zhanjiang,Guangdong,524048,P.R.China) |
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| Abstract: | Let n be an odd integer with n>3.In this paper,using a recent result on the existence of primitive divisors of Lehmer numbers given by Y.Bilu,G.Hanrot and P.M. Voutier,we prove that the equation nx~2 + 2~m = y~n has no positive integer solution(x,y,m) satisfying gcd(x,y) = 1 and m is odd. |
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| Keywords: | exponential diophantine equation Lehmer number primitive divisor |
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