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Found problems: 1

2018 USAMO, 3
Tags: USAMO , 2018 USAMO Problem 3 , number theory , Hi
For a given integer $n\ge 2$, let $\{a_1,a_2,…,a_m\}$ be the set of positive integers less than $n$ that are relatively prime to $n$. Prove that if every prime that divides $m$ also divides $n$, then $a_1^k+a_2^k + \dots + a_m^k$ is divisible by $m$ for every positive integer $k$. [i]Proposed by Ivan Borsenco[/i]