MathDB

C1

Part of 2019 JBMO Shortlist

Problems(1)

JBMO Shortlist 2019 C1

Source:

9/12/2020
Let SS be a set of 100100 positive integer numbers having the following property: “Among every four numbers of SS, 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 SS contains a number which divides all other 9999 numbers of SS.
Proposed by Tajikistan
combinatorics