Difference between revisions of "2006 Romanian NMO Problems/Grade 8/Problem 2"

Revision as of 10:33, 27 July 2006

Let $n$ be a positive integer. Prove that there exists an integer $k$ , $k\geq 2$ , and numbers $a_i \in \{ -1, 1 \}$ , such that

$n = \sum_{1\leq i < j \leq k } a_ia_j$ .