CAPS 1995 Problem 6

Find all triples $(x; y; p)$ of two non-negative integers $x, y$ and a prime number p such that $p^x-y^p=1$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.