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x+y in B iff x,y in A

Source: China Mathematical Olympiad 2015 Q3

December 20, 2014
absolute valuecombinatorics proposedcombinatorics

Problem Statement

Let n≥5n \geq 5 be a positive integer and let AA and BB be sets of integers satisfying the following conditions:
i) ∣A∣=n|A| = n, ∣B∣=m|B| = m and AA is a subset of BB ii) For any distinct x,y∈Bx,y \in B, x+y∈Bx+y \in B iff x,y∈Ax,y \in A
Determine the minimum value of mm.
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