An elementary approach to the generalized Ramanujan-Nagell equation

2023/01/13 by Elif Kızıldere Mutlu, Mutlu, Elif Kızıldere, LE Mao-hua +3
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2301.05431

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 x²+(2k-1)^y=k^z has no positive integer solutions (x,y,z) with y∈\3,5\.

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