OPENHARDnumber theorySidon setsadditive combinatorics
Let $A\subset \{1,\ldots,N\}$ be a Sidon set. For any $\epsilon>0$, do there exist $M$ and $B\subset \{N+1,\ldots,M\}$ such that $A\cup B$ is a Sidon set of size at least $(1-\epsilon)M^{1/2}$?
Notes: A positive solution to problem 707 would imply this, which in turn implies problem 329.
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