On the exponential Diophantine equation x^2+p^{2m}=2y^{n}

Authors

  • Huilin Zhu
  • Maohua Le
  • Alain Togbe

Keywords:

Exponential Diophantine equation, Lehmer number, Primitive divisor.

Abstract

Let $p$ be an odd prime. In this paper, we consider the equation $x^{2}+p^{2m}=2y^{n},~\gcd(x,y)=1,n>2$ and we give a description for all its solutions. Moreover, we prove that this equation has no solution $(x,y,m,n)$ such that $n>3$ is an odd prime and $y$ is not the sum of two consecutive squares. This extends the work of Tengely. DOI: 10.1017/S000497271200010X

Author Biography

Huilin Zhu

Published

2012-08-27

Issue

Vol. 86 No. 2 (2012)

Section

Articles
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