Abstract
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.
Keywords
Diophantine equation
Integer (computer science)
Exponential function
Mathematics
Divisor (algebraic geometry)
Diophantine set
Discrete mathematics
Combinatorics
Mathematical analysis
Computer science
Subject Areas
Algebraic Geometry and Number Theory
·Geometry and Topology ·Physical Sciences
Analytic Number Theory Research
·Algebra and Number Theory ·Physical Sciences
Mathematical Dynamics and Fractals
·Mathematical Physics ·Physical Sciences
Citations by Year
2015: 1
2022: 1
2024: 2
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