On the Diophantine equation nx2+22m = yn

JOURNAL OF NUMBER THEORY

卷:131

Article

Wang Yongxing¹  Wang Tingting² 

[1] Weinan Teachers Univ, Dept Math & Informat, Xian, Shaanxi, Peoples R China

[2] Northwest Univ, Dept Math, Xian, Shaanxi, Peoples R China

关键词: Exponential Diophantine equation;    Lehmer number;    Primitive divisor;   

DOI  :  10.1016/j.jnt.2011.02.014

来源: Elsevier

【 摘 要 】

Let n be a fixed odd integer with n > 1. In this paper, using a recent result on the existence of primitive divisors of Lehmer numbers give by Y. Bilu, G. Hanrot and P.M. Voutier, we prove that the equation nx(2) + 2(2m) = y(n) has no positive integer solution (x, y, m) with gcd(x, y) = 1. (C) 2011 Published by Elsevier Inc.

【 授权许可】

Free