Question 20
Let $p$ be a prime number, and let $x$ and $n$ be integers such that $1 \le x \lt n$. We have $x + 1$ different boxes and $n - x$ identical balls. Let us call $f(n,x)$ the number of ways in which one can distribute the $n - x$ into the $x + 1$ boxes. Find all integers $n$ greater than $1$ such that $p$ divides $f(n,x)$ for every $x \in \{1,2,...,n\}$