2018 USAMO Problems/Problem 3

Problem 3

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 $k.$

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2018 USAMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
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2018 USAMO Problems/Problem 3

Problem 3

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