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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}.

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