JBMO Shortlist 2019 C1
Source:
September 12, 2020
combinatorics
Problem Statement
Let be a set of positive integer numbers having the following property:
“Among every four numbers of , there is a number which divides each of the other three
or there is a number which is equal to the sum of the other three.”
Prove that the set contains a number which divides all other numbers of .Proposed by Tajikistan