Competition problem — Number theory

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Number theory Difficulty 5.9 AIME, harder Prove it

Property 3 If $a \equiv b(\bmod m), n$ is a positive integer, then $a^{n} \equiv b^{n}(\bmod m)$ .

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.