A note on the Diophantine equations $x^{2}\pm5^{\alpha}\cdot p^{n}=y^{n}$

Gökhan Soydan

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arXiv · 1706.03185

A note on the Diophantine equations $x^{2}\pm5^{\alpha}\cdot p^{n}=y^{n}$

Gökhan Soydan

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Abstract

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 $gcd(x,y)=1$.

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BibTeX RIS

Gökhan Soydan. 2017-06-10. A note on the Diophantine equations $x^{2}\pm5^{\alpha}\cdot p^{n}=y^{n}$. https://arxiv.org/abs/1706.03185

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