arXiv subjects

Yongzhong Hu

Publications and source records attributed to Yongzhong Hu.

2 recordsLinked to original sources

arXiv2018

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

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 $(x,y,z)$.

math.NT↗

arXiv2017

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

Let $a,b,c$ be fixed coprime positive integers with $\min\{a,b,c\}>1$. In this paper, combining the Gel'fond-Baker method with an elementary approach, we prove that if $\max\{a,b,c\}>5\times 10^{27}$, then the equation $a^x+b^y=c^z$ has at most three positive integer solutions $(x,y,z)$.

math.NT↗