Difference between revisions of "2006 Romanian NMO Problems/Grade 8/Problem 2"
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Let <math>n</math> be a positive integer. Prove that there exists an integer <math>k</math>, <math>k\geq 2</math>, and numbers <math>a_i \in \{ -1, 1 \}</math>, such that <center><math>n = \sum_{1\leq i < j \leq k } a_ia_j</math>.</center> | Let <math>n</math> be a positive integer. Prove that there exists an integer <math>k</math>, <math>k\geq 2</math>, and numbers <math>a_i \in \{ -1, 1 \}</math>, such that <center><math>n = \sum_{1\leq i < j \leq k } a_ia_j</math>.</center> | ||
==Solution== | ==Solution== | ||
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==See also== | ==See also== | ||
*[[2006 Romanian NMO Problems]] | *[[2006 Romanian NMO Problems]] | ||
[[Category:Olympiad Number Theory Problems]] | [[Category:Olympiad Number Theory Problems]] | ||
Revision as of 08:32, 27 August 2008
Problem
Let 
be a positive integer. Prove that there exists an integer 
, 
, and numbers 
, such that
.Solution
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