China TST $2011$ Quiz 3 Day 1

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rah4927
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China TST $2011$ Quiz 3 Day 1

Unread post by rah4927 » Mon Aug 15, 2016 6:40 pm

Let $n>1$ be an integer, and let $k$ be the number of distinct prime divisors of $n$. Prove that there exists an integer $a$, $1<a<\frac{n}{k}+1$, such that $n \mid a^2-a$.

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