IMO 1966 LL CZS42

Let a1, a2, . . . , an (n \geq2) be a sequence of integers. Show that

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IMO 1966 LL CZS42

Origin: CZS

Problem

Let a1, a2, . . . , an (n \geq2) be a sequence of integers. Show that there is a subsequence ak1, ak2, . . . , akm, where 1 \leqk1 < k2 < \cdot \cdot \cdot < km \leq n, such that a2 k1 + a2 k2 + \cdot \cdot \cdot + a2 km is divisible by n.