Determine all integers such that every with divides the binomial coefficient .
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Determine all integers $m \geq 2$ such that every $n$ with $\frac{m}{3} \leq n \leq \frac{m}{2}$ divides the binomial coefficient $\binom{n}{m-2n}$.
Source: Međunarodna matematička olimpijada, shortlist 2012
Školjka 
such that every 
with 
divides the binomial coefficient 
.