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Sets include the sum or the difference of every two elements

Source: Argentina TST IMO 2006 Problem 1

July 22, 2008
combinatorics proposedcombinatorics

Problem Statement

Let A A be a set of natural numbers in which if a a , b b belong to A A (a>b a>b) then either a\plus{}b or a\minus{}b belong to A A ( both cases may be posible at the same time). Decide wheter there is or not a set A A consisting on exactly 100 100 elements which has four elements x x, y y , z z , w w ( not necesarilly distinct) that satisfy x\minus{}y\equal{}512 and z\minus{}w\equal{}460 Daniel
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