Problem

Source: Chinese TST

Tags: combinatorics proposed, combinatorics



Prove that for arbitary integer $ n > 16$, there exists the set $ S$ that contains $ n$ positive integers and has the following property:if the subset $ A$ of $ S$ satisfies for arbitary $ a,a'\in A, a\neq a', a + a'\notin S$ holds, then $ |A|\leq4\sqrt n.$