On the Diophantine Equation a^x+(a+2)^y=z^2 - Tadee, Suton (KKU Science Journal, 2024)
In this paper, we investigated the solutions of the Diophantine equation , where is a positive integer and are non-negative integers. Let be the set of non-negative integer solutions of the equation. The results showed that 1) if is a prime number with , then , where is an integer, otherwise . 2) If is a prime number and is even and the equation has a solution, then and . 3) Let be a prime number such that and . Then , where is an integer, otherwise , when it satisfies one of the following cases: case 1 or case 2 there exists a prime number such that and .