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Let $F(N)$ be the size of the largest Sidon subset of $\{1,\ldots,N\}$. Is it true that for every $k\geq 1$ we have \[F(N+k)\leq F(N)+1\] for all sufficiently large $N$?
#155
:
[Er92c]
[ESS94]
[Er94b]
additive combinatorics
,
sidon sets
This may even hold with $k\approx \epsilon N^{1/2}$.
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