在美元指数丢番图方程(6米^ {2}+ 1)^ {x} + (3 m ^ {2} 1) ^ {y} =(3米)^ {z} $

Fundamental Journal of Mathematics and Applications Pub Date : 2022-06-29 DOI:10.33401/fujma.1038699

M. Alan, Ruhsar Gizem Bi̇ratli

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引用次数: 4

摘要

设m为正整数。本文考虑指数丢芬图方程$(6m^{2}+1)^{x}+(3m^{2}-1)^{y}=(3m)^{z}$，并证明对于所有$ m>1，它只有唯一的正整数解$(x,y,z)=(1,1,2)$。这个证明依赖于所谓的分类方法和著名的原始因子定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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 so called classification method and famous primitive divisor theorem.

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Fundamental Journal of Mathematics and Applications

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