Extended inverse theorems for $h$-fold sumsets in integers
DOI:
https://doi.org/10.55016/ojs/cdm.v18i2.73074Abstract
Let $h \geq 2$, $k \geq 5$ be integers and $A$ be a nonempty finite set of $k$ integers. Very recently, Tang and Xing studied extended inverse theorems for $hk-h+1 < \left|hA\right| \leq hk+2h-3$. In this paper, we extend the work of Tang and Xing and study all possible inverse theorems for $hk-h+1<\left|hA\right| \leq hk+2h +1$. Furthermore, we give a range of $|hA|$ for which inverse problems are not possible.
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