IMO 1984 LL ROM49

Let n > 1 and xi \inR for i = 1, . . . , n. Set Sk = xk

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IMO 1984 LL ROM49

Origin: ROM

Problem

Let n > 1 and xi \inR for i = 1, . . . , n. Set Sk = xk 1 + xk 2 + \cdot \cdot \cdot + xk n for k \geq1. If S1 = S2 = \cdot \cdot \cdot = Sn+1, show that xi \in{0, 1} for every i = 1, 2, . . ., n.