On the Diophantine Equation 7x-2y=z2 where x, y and z are Non-Negative Integers

In this article, we prove all solutions of the exponential Diophantine equation 2 7 2 x y − = z where x y, and z are non-negative integers. The mathematical principles are applied to obtain the solutions such as factoring method modular arithmetic method and Catalan’s conjecture. The result reveals that there is only a trivial solution to the equation.