20

Part of 1988 IMO Shortlist

Problems(1)

Two non-intersecting subsets

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

Find the least natural number

n

such that, if the set

\{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.

combinatoricspartitionColoringExtremal combinatoricsRamsey TheoryIMO Shortlist