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2006 Romanian NMO Problems/Grade 8/Problem 2

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Problem

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

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

Solution

See also

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