2012 IMO Shortlist N3

Determine all integers $m \geq 2$ such that every $n$ with $\frac{m}{3} \leq n \leq \frac{m}{2}$ divides the binomial coefficient $\left(\begin{array}{c}n \\ m-2 n\end{array}\right)$.

确定所有整数 $m \geq 2$，使得每个 $n$ 与 $\frac{m}{3} \leq n \leq \frac{m}{2}$ 除二项式系数 $\left(\begin{array}{c}n \\ m-2 n\end{array}\right)$。