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A U B = N (combinatorics)

Source: Federation of Bosnia, 1. Grades 2008.

April 23, 2008

Problem Statement

Given are two disjoint sets A A and B B such that their union is N \mathbb N. Prove that for all positive integers n n there exist different numbers a a and b b, both greater than n n, such that either \{ a,b,a \plus{} b \} is contained in A A or \{ a,b,a \plus{} b \} is contained in B B.
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