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arXiv · 1808.06272

An Upper Bound for the Number of Solutions of Ternary Purely Exponential Diophantine Equations II

Yongzhong Hu·Maohua Le
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Abstract

Let $a,b,c$ be fixed coprime positive integers with $\min\{a,b,c\}>1$. In this paper, by analyzing the gap rule for solutions of the ternary purely exponential diophantine equation $a^x+b^y=c^z$, we prove that if $\max\{a,b,c\}\geq 10^{62}$, then the equation has at most two positive integer solutions $(x,y,z)$.

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Yongzhong Hu, Maohua Le. 2018-08-19. An Upper Bound for the Number of Solutions of Ternary Purely Exponential Diophantine Equations II. https://arxiv.org/abs/1808.06272

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