IMO 1985 LL FRA25

Find eight positive integers n1, n2, . . . , n8 with the follow-

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IMO 1985 LL FRA25

Origin: FRA

Problem

Find eight positive integers n1, n2, . . . , n8 with the follow- ing property: For every integer k, −1985 \leqk \leq1985, there are eight integers \alpha1, \alpha2, . . . , \alpha8, each belonging to the set {−1, 0, 1}, such that k = 8 i=1 \alphaini.