When is the binomial co-efficient divisible ?

Determine the number of integers \(m\) such that \(2≤m≤946\) and every integer \(n\) with \(\frac{m}{3}≤n≤\frac{m}{2}\) divides the binomial co-efficient \(\binom{n}{m-2n}\).

This is a IMO problem.

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