More on the Diophantine equation 3ˣ + 85ʸ = z²

In this paper, we show that (1, 0, 2) is a unique non-negative integer solution (x, y, z) for the Diophantine equation 3 x + 85 y = z 2 where x, y and z are non-negative integers. This result implies that (1, 0, 0, 2) is a solution (x, u, v, z) for the Diophantine equation 3 x + 5 u 17 v = z 2 .