An upper bound for the number of solutions of ternary purely exponential Diophantine equations. II

Let $a$, $b$, $c$ be fixed pairwise 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 $(x,y,z)$.