## China TST $2011$ Quiz 3 Day 1

For discussing Olympiad Level Number Theory problems
rah4927
Posts: 108
Joined: Sat Feb 07, 2015 9:47 pm

### China TST $2011$ Quiz 3 Day 1

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 $n \mid a^2-a$.