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Turkish Journal of Mathematics

DOI

10.55730/1300-0098.3153

Abstract

Let $a,b,c$ be fixed positive integers such that $a+b=c^2$, $2 \nmid c$ and $(b/p)\ne 1$ for every prime divisor $p$ of $c$, where $(b/p)$ is the Legendre symbol. Further let $m$ be a positive integer with $m>1$. In this paper, using the Baker method, we prove that if $m>\max\{10^8,c^2\}$, then the equation $(am^2+1)^x+(bm^2-1)^y=(cm)^z$ has only one positive integer solution $(x,y,z)=(1,1,2)$.

First Page

1224

Last Page

1232

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Mathematics Commons

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