IT-CESENATICO 2011 Problem 5

Determine all solutions $(p,n)$ of the equation $n^3=p^2-p-1$ where $p$ is a prime number and $n$ is an integer

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.