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2018 USAMO Problems/Problem 3

Revision as of 11:51, 21 April 2018 by Sujaykazi (talk | contribs) (Created page with "==Problem 3== For a given integer <math>n\ge 2,</math> let <math>\{a_1,a_2,…,a_m\}</math> be the set of positive integers less than <math>n</math> that are relatively prime...")
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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 $k.$


Solution

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