MathDB
Set exists where subsets satisfying a condition are small

Source: Chinese TST

April 5, 2008
combinatorics proposedcombinatorics

Problem Statement

Prove that for arbitary integer n>16 n > 16, there exists the set S S that contains n n positive integers and has the following property:if the subset A A of S S satisfies for arbitary a,a'\in A, a\neq a', a \plus{} a'\notin S holds, then ∣A∣≤4n. |A|\leq4\sqrt n.
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