On the Exponential Diophantine Equation ( ) ( ) x y p p z + + + = 2 2 5 6 when p p, + 2 and 5 6 p+ are Primes

Abstract

In this work, we prove that the exponential Diophantine equation ( ) ( ) 2 2 5 6 x y p p z + + + = has no solution when p p, 2 + and 5 6 p + are primes, and x y z , , are non-negative integers.