Definition: For any x \in \mathbb{R} and integer k \geq 0 we define \binom{x}{0}=1 and \binom{x}{k}=\frac{x(x-1) \cdots (x-k+1)}{k!}, \ \ k \geq 1.

Prove that for any integers m,n,k, where k \geq 0 and n \geq 1, we have: \binom{\frac{m}{n}}{k} \in \mathbb{Z}[1/n].