Gökhan Soydan
Published 2017-06-10Version 1
Suppose that $x$ is odd, $n\geq7$ and $p\notin\{2,5\}$ are primes. In this paper, we prove that the Diophantine equations $x^{2}\pm5^{\alpha}p^{n}=y^{n}$ have no solutions in positive integers $\alpha,x,y$ with $gcd(x,y)=1$.
Comments: 8 pages, accepted for publication in Commun. Fac. Sci. Univ. Ank. Series A1: Math. and Stat
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