I'm Trying to find all integer solutions of the diophantine equation:
where $p$ is a prime number $p\equiv 13 \quad or\quad 17 \quad (\mod 20)$.
I know that $y=0$ is a solution of this. I think this is the only solution, but I can't prove this fact.
Can you help me to prove this claim if it's true, and to find all solutions otherwise.