IMO 1996 Problem 3

Let $p,q,n$ be three positive integers with $p + q < n$ . Let $(x_{0},x_{1},\cdots ,x_{n})$ be an $(n + 1)$ -tuple of integers satisfying the following conditions :

(a) $x_{0} = x_{n} = 0$ , and

(b) For each $i$ with $1\leq i\leq n$ , either $x_{i} - x_{i - 1} = p$ or $x_{i} - x_{i - 1} = - q$ .

Show that there exist indices $i < j$ with $(i,j)\neq (0,n)$ , such that $x_{i} = x_{j}$ .