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Two non-intersecting subsets

Source: IMO ShortList 1988, Problem 20, Mongolia 4, Problem 54 of ILL

November 3, 2005
combinatoricspartitionColoringExtremal combinatoricsRamsey TheoryIMO Shortlist

Problem Statement

Find the least natural number n n such that, if the set {1,2,…,n} \{1,2, \ldots, n\} is arbitrarily divided into two non-intersecting subsets, then one of the subsets contains 3 distinct numbers such that the product of two of them equals the third.
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