Let $p$ be an odd prime number. Prove that there exists a unique integer $k$ such that $0 \le k \le p^2$ and $p^2$ divides $k(k + 1)(k + 2) ... (k + p - 3) - 1$. Malik Talbi
Source: 2015 Saudi Arabia GMO TST I p4
Tags: number theory, divides, divisible
Let $p$ be an odd prime number. Prove that there exists a unique integer $k$ such that $0 \le k \le p^2$ and $p^2$ divides $k(k + 1)(k + 2) ... (k + p - 3) - 1$. Malik Talbi