FKMO 2007 Problem 4

Find all pairs $(p, q)$ of primes such that ${p}^{p}+{q}^{q}+1$ is divisible by $pq$ .

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.