IMO 2013 Shortlist N2

Prove that for any pair of positive integers k and n there exist k positive integers m1,m2,...,mk such that 1 2k ´ 1 n “...

IMO 2013 Shortlist N2

Category: Number Theory

Problem

Prove that for any pair of positive integers k and n there exist k positive integers m1,m2,...,mk such that 1 2k ´ 1 n “ ˆ 1 m1 ˙ˆ 1 m2 ˙ ¨¨¨ ˆ 1 mk ˙ . (Japan)