MathDB

A3

Part of 2018 IMO Shortlist

Problems(1)

Showing properties about subsets of positive integers.

Source: IMO 2018 Shortlist A3

7/17/2019
Given any set SS of positive integers, show that at least one of the following two assertions holds:
(1) There exist distinct finite subsets FF and GG of SS such that ∑x∈F1/x=∑x∈G1/x\sum_{x\in F}1/x=\sum_{x\in G}1/x;
(2) There exists a positive rational number r<1r<1 such that ∑x∈F1/x≠r\sum_{x\in F}1/x\neq r for all finite subsets FF of SS.
algebraIMO Shortlistrational numberSets