AUSTRIAN-POLISH 1982 Problem 1

Find all pairs $(n, m)$ of positive integers such that $gcd ((n + 1)^m - n, (n + 1)^{m+3} - n) > 1$ .

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.