IMO 2018 Shortlist A3
Given any set S of positive integers, show that at least one of the following two assertions holds: (1) There exist dist...
Category: Algebra
Problem
Given any set S of positive integers, show that at least one of the following two assertions holds: (1) There exist distin t nite subsets F and G of S su h that ř xPF 1{x “ ř xPG 1{x; (2) There exists a positive rational number r ă 1 su h that ř xPF 1{x ‰ r for all nite subsets F of S. (Luxembourg)