Solution of the Diophantine equation ${783}^x+{85}^y=z^2$∗

Abstract

In this paper we consider the Diophantine equation ${783}^x+{85}^y=z^2$, where $x,y,z$ are non-negative integers and determine the non-negative integer solutions of this equation. Our result shows that $(x, y, z) = (1, 0, 28)$  is a unique non-negative integer solution of this equation.