OPENHARDnumber theorySidon setsadditive combinatorics
Let $A \subset \mathbb{N}$ and $B$ be the set of integers representable in exactly one way as the sum of two elements from $A$. Is it true that $|\{1,\ldots,N\} \setminus B| \gg_\epsilon N^{1/2-\epsilon}$ for all $\epsilon > 0$? Is $|\{1,\ldots,N\} \setminus B| = o(N^{1/2})$ possible?
Notes: Erdos, Sarkozy, and Szemeredi constructed A where |{1,...,N} \ B| << N^{1/2+epsilon} yet infinitely often >> N^{1/3-epsilon}.
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