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Complete Residue System

Source: 2020 China North Mathematical Olympiad Advanced Level P3

August 4, 2020

number theorymoduloresidue

Problem Statement

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