Let $ p>3$ be a prime. If $ p$ divides $ x$, prove that the equation $ x^2-1=y^p$ does not have positive integer solutions.
Problem
Source: Oliforum Contest I 2008 2.1 https://artofproblemsolving.com/community/c2487525_oliforum_contes
Tags: diophantine, Diophantine equation, number theory