IMO Shortlist 2012 problem N3
Dodao/la:
arhiva3. studenoga 2013. Determine all integers
![m \geq 2](/media/m/b/c/5/bc5c7c47b94157dbd3e0f8bf5a87150b.png)
such that every
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
with
![\frac{m}{3} \leq n \leq \frac{m}{2}](/media/m/5/0/a/50ad4bc16e88ecfebac0867db4b837ff.png)
divides the binomial coefficient
![\binom{n}{m-2n}](/media/m/a/4/1/a41b181d7b784ebd74e56d6104124bea.png)
.
%V0
Determine all integers $m \geq 2$ such that every $n$ with $\frac{m}{3} \leq n \leq \frac{m}{2}$ divides the binomial coefficient $\binom{n}{m-2n}$.
Izvor: Međunarodna matematička olimpijada, shortlist 2012