On the Non-Linear Diophantine Equation 61ˣ + 67ʸ = z² and 67ˣ + 73ʸ = z²

In this paper, we consider the non-linear Diophantine equations 61 x + 67 y = z 2 and 67 x + 73 y = z 2 , where x, y and z are non-negative integers. It has been shown that these non-linear Diophantine equations have no solution.