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arXiv · 2301.05431

An elementary approach to the generalized Ramanujan-Nagell equation

Elif Kızıldere Mutlu·Maohua Le·Gökhan Soydan
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Abstract

Let $k$ be a fixed positive integer with $k>1$. In this paper, using various elementary methods in number theory, we give criteria under which the equation $x^2+(2k-1)^y=k^z$ has no positive integer solutions $(x,y,z)$ with $y\in\{3,5\}$.

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Elif Kızıldere Mutlu, Maohua Le, Gökhan Soydan. 2023-01-13. An elementary approach to the generalized Ramanujan-Nagell equation. https://arxiv.org/abs/2301.05431

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