Maths Olympiad Prep

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Number theory Difficulty 5.9 AIME, harder Prove it

5. Show that if nn is a positive integer having kk distinct odd prime divisors, then ϕ(n)\phi(n) is divisible by 2k2^{k}.

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.