OME 2012 Problem 3

Let $x$ and $n$ be integers such that $1\le x\le n$ . We have $x+1$ separate boxes and $n-x$ identical balls. Define $f(n,x)$ as the number of ways that the $n-x$ balls can be distributed into the $x+1$ boxes. Let $p$ be a prime number. Find the integers $n$ greater than $1$ such that the prime number $p$ is a divisor of $f(n,x)$ for all $x\in\{1,2,\ldots ,n-1\}$ .