An elementary approach to the generalized Ramanujan-Nagell equation

Published 13 Jan 2023 in math.NT | (2301.05431v1)

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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