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JBMO 2018. Shortlist Algebra

Source:

July 11, 2019
algebraSubsetsSetscardinality

Problem Statement

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 ?
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