Competition problem — Number theory

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Number theory Difficulty 5.7 AIME, harder Prove it

12. Show that a positive integer $n$ is composite if and only if $\phi(n) \leqslant n-\sqrt{n}$ .

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.