IMO 1988 LL POL71

Given integers a1, . . . , a10, prove that there exists a nonzero

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IMO 1988 LL POL71

Origin: POL

Problem

Given integers a1, . . . , a10, prove that there exists a nonzero sequence (x1, . . . , x10) such that all xi belong to {−1, 0, 1} and the number 10 i=1 xiai is divisible by 1001.