On Freiman-Lev conjecture
Abstract
Let $A$ be a set of $k$ integers such that $A\subseteq [0, l]$, $0, l\in A$ and $\gcd(A)=1$. Let $2^{\wedge}A$ denote the set of all sums of two distinct elements of $A$. Write $W=\{w\in [0, l]\backslash A: w,w+l\not\in 2^{\wedge}A\}$. In this paper, we obtain the upper bound of $|W|$ with some restrictions on $l$. As an application, we show that the Freiman-Lev conjecture is true for $l=2k-4$ using the structure of $A$ with $|W|=2$.
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