Question 70
Let $x,n$ be integers with $1\le x\lt n$. There are $x+1$ distinct boxes and $n-x$ identical balls. Let $f(n,x)$ be the number of ways to distribute the balls among the boxes. Given a prime $p$, find all integers $n\gt 1$ such that $p$ divides $f(n,x)$ for every $x\in\{1,2,\dots,n-1\}$.