On the exponential Diophantine equation (3m2+1)x+(qm2−1)y=(rm)z

Nobuhiro Terai; Yoshiki Shinsho

doi:10.55937/sut/1611009430

December 2020 On the exponential Diophantine equation

(3m^2 + 1)^x + (qm^2 - 1)^y = (rm)^z

Nobuhiro Terai, Yoshiki Shinsho

Author Affiliations +

SUT J. Math. 56(2): 147-158 (December 2020). DOI: 10.55937/sut/1611009430

Abstract

Let $m, q, r$ be positive integers. Then we show that the equation $(3m^2 + 1)^x + (qm^2 - 1)^y = (rm)^z$ has only the positive integer solution $(x,y,z) = (1,1,2)$ under some conditions. The proof is based on elementary methods and Baker’s method.

Funding Statement

The first author is supported by JSPS KAKENHI Grant (No.18K03247).

Citation

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Nobuhiro Terai. Yoshiki Shinsho. "On the exponential Diophantine equation $(3m^2 + 1)^x + (qm^2 - 1)^y = (rm)^z$ ." SUT J. Math. 56 (2) 147 - 158, December 2020. https://doi.org/10.55937/sut/1611009430