IMO 2013 Q1 #
Prove that for any pair of positive integers k and n, there exist k positive integers m₁, m₂, ..., mₖ (not necessarily different) such that
1 + (2ᵏ - 1)/ n = (1 + 1/m₁) * (1 + 1/m₂) * ... * (1 + 1/mₖ).
Adaptation of the solution found in https://www.imo-official.org/problems/IMO2013SL.pdf
We prove a slightly more general version where k does not need to be strictly positive.