International Mathematical Olympiad 1996 Problem 6

Let $p, q, n$ be three positive integers with $p + q < n$. Let $(x_0, x_1, \ldots, x_n)$ be an $(n + 1)$-tuple of integers satisfying the following conditions:

(a) $x_0 = x_n = 0$.

(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 $x_i = x_j$.