MathDB

25

Part of 1985 IMO Longlists

Problems(1)

Find eight positive integers

Source:

9/13/2010
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 .
number theory unsolvednumber theory