On the Exponential Diophantine Equation $(6m^{2}+1)^{x}+(3m^{2}-1)^{y}=(3m)^{z}$

Yıl 2022, Cilt: 5 Sayı: 3, 174 - 180, 23.09.2022

Murat Alan Ruhsar Gizem Biratlı

https://doi.org/10.33401/fujma.1038699

Cited By: 1

Öz

Let $m$ be a positive integer. In this paper, we consider the exponential Diophantine equation $(6m^{2}+1)^{x}+(3m^{2}-1)^{y}=(3m)^{z}$ and we show that it has only unique positive integer solution $(x,y,z)=(1,1,2)$ for all $ m>1. $ The proof depends on some results on Diophantine equations and the famous primitive divisor theorem.

Anahtar Kelimeler

Classification method, Exponential Diophantine equations, Primitive divisor theorem, Terai’s conjecture

Proje Numarası

4141

Kaynakça

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