Školjka

%V0 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 $x_{i} = x_{j}$.