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

 
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==See also==
 
==See also==
 
*[[2006 Romanian NMO Problems]]
 
*[[2006 Romanian NMO Problems]]
 +
[[Category:Olympiad Number Theory Problems]]

Revision as of 10:07, 28 July 2006

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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