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Eccentricity in the number of representations for sets too large to be Sidon sets

There exists a set $A$ on $\{1,...,N\}$ where $ |A|\geq\frac{2}{\sqrt{3}}\sqrt{N}$ and $E(A)=o(N)$. Let $B$ be a Sidon set on $\{1,...,n\}$. Let $C = \{3n+1-b | b\in B\}$. Let $A=B\cup C$. Suppose $ …
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