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Good Partitions

Source: 2015 ISL C3

July 7, 2016
greatest common divisorcombinatoricsIMO Shortlist

Problem Statement

For a finite set AA of positive integers, a partition of AA into two disjoint nonempty subsets A1A_1 and A2A_2 is <spanclass=′latex−italic′>good</span><span class='latex-italic'>good</span> if the least common multiple of the elements in A1A_1 is equal to the greatest common divisor of the elements in A2A_2. Determine the minimum value of nn such that there exists a set of nn positive integers with exactly 20152015 good partitions.
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