SOLUTION OF THE EXPONENTIAL DIOPHANTINE EQUATION.
In this research, we consider the Diophantine equation 8x 131y z2 where x, y and z
were non-negative integers. This study aims at obtaining the solution of this equation.
Catalan’s conjecture is used to solve the solution. To propose Catalan’s conjecture for the Diophantine equation 1 x y a b that has a unique solution. We have exactly solution x, y, z in non-negative integers and find that it has a unique solution, that is x, y, z 1,0,3 Then, we prove that (1,0,3) is a unique non-negative integer solution of this Diophantine equation.