Problem

Source: 2020 China North Mathematical Olympiad Advanced Level P3

Tags: number theory, modulo, residue



A set of $k$ integers is said to be a complete residue system modulo $k$ if no two of its elements are congruent modulo $k$. Find all positive integers $m$ so that there are infinitely many positive integers $n$ wherein $\{ 1^n,2^n, \dots , m^n \}$ is a complete residue system modulo $m$.