On a conjecture on exponential Diophantine equations

Mihai Cipu, Maurice Mignotte

We study the solutions of a Diophantine equation of the form $a^x+b^y=c^z$, where $a\equiv 2(\mathrm{mod}4)$, $b\equiv 3(\mathrm{mod}4)$ and $\gcd (a,b,c)=1$. The main result is that if there ex…