MK-MO 2023 Problem 2

Let $p$ and $q$ be odd prime numbers and $a$ a positive integer so that $p|a^q+1$ and $q|a^p+1$ . Show that $p|a+1$ or $q|a+1$ .

Authored by Nikola Velov

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.