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Let $a,b,c$ be fixed coprime positive integers with $\min\{a,b,c\}>1$. Inthis paper, by analyzing the gap rule for solutions of the ternary purelyexponential 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 integersolutions $(x,y,z)$.

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