This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2011 Turkey MO (2nd round), 4
Tags: number theory , legendre s theorem , modular arithmetic
$a_{1}=5$ and $a_{n+1}=a_{n}^{3}-2a_{n}^{2}+2$ for all $n\geq1$. $p$ is a prime such that $p=3(mod 4)$ and $p|a_{2011}+1$. Show that $p=3$.

2015 China Second Round Olympiad, 4
Tags: legendre s theorem , number theory
Find all positive integers $k$ such that for any positive integer $n$, $2^{(k-1)n+1}$ does not divide $\frac{(kn)!}{n!}$.