NL-NWO 2012 Problem 3

Determine all pairs $(p,m)$ consisting of a prime number $p$ and a positive integer $m$ , for which $p^3 + m(p + 2) = m^2 + p + 1$ holds.

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.