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Find eight positive integers

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September 13, 2010
number theory unsolvednumber theory

Problem Statement

Find eight positive integers n1,n2,…,n8n_1, n_2, \dots , n_8 with the following property:
For every integer kk, −1985≤k≤1985-1985 \leq k \leq 1985, there are eight integers a1,a2,…,a8a_1, a_2, \dots, a_8, each belonging to the set {−1,0,1}\{-1, 0, 1\}, such that k=∑i=18aini.k=\sum_{i=1}^{8} a_i n_i .
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