MathDB

A7

Part of 2018 JBMO Shortlist

Problems(1)

JBMO 2018. Shortlist Algebra

Source:

7/11/2019
Let AA be a set of positive integers satisfying the following :
a.)a.) If n∈An \in A , then n≤2018n \le 2018.
b.)b.) If S⊂AS \subset A such that ∣S∣=3|S|=3, then there exists m,n∈Sm,n \in S such that ∣n−m∣≥n+m|n-m| \ge \sqrt{n}+\sqrt{m}
What is the maximum cardinality of AA ?
algebraSubsetsSetscardinality