Find all pairs $(n, q)$ such that $n$ is a positive integer, $q$ is a not integer rational and $$n^q-q$$is an integer.
Problem
Source: OMEC Ecuador National Olympiad Final Round 2020 N3 P2 day 1
Tags: number theory, national olympiad
Source: OMEC Ecuador National Olympiad Final Round 2020 N3 P2 day 1
Tags: number theory, national olympiad
Find all pairs $(n, q)$ such that $n$ is a positive integer, $q$ is a not integer rational and $$n^q-q$$is an integer.