US-TST 2003 Problem 3

Find all ordered triples of primes $(p, q, r)$ such that $p \mid q^r + 1, q \mid r^p + 1, r \mid p^q + 1.$ Reid Barton

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.