General Solution of the Diophantine equation involving Mersenne Prime

In this article, I study and solve the exponential Diophantine equation $M_p^x+(M_q+1{)}^y=(lz{)}^2$ where $M_p$ and $M_q$ are Mersenne primes, $l$ is a prime number, and $x,y$, and $z$ are non-negative integers. Several illustrations are presented as well as cases where no solution of the given Diophantine equation is present.