IMO 2015 Shortlist C3
For a finite set A of positive integers, we call a partition of A into two disjoint nonempty subsets A1 and A2 good if t...
Category: Combinatorics
Problem
For a finite set A of positive integers, we call a partition of A into two disjoint nonempty subsets A1 and A2 good if the least common multiple of the elements in A1 is equal to the greatest common divisor of the elements in A2. Determine the minimum value of n such that there exists a set of n positive integers with exactly 2015 good partitions. (Ukraine)