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 Some inverse results of sumsets Bull. Korean Math. Soc. 2021 Vol. 58, No. 2, 305-313 https://doi.org/10.4134/BKMS.b200054Published online March 5, 2021Printed March 31, 2021 Min Tang, Yun Xing Anhui Normal University; Anhui Normal University Abstract : Let $h\geq 2$ and $A=\{a_0,a_1,\ldots,a_{k-1}\}$ be a finite set of integers. It is well-known that $\left|hA\right|=hk-h+1$ if and only if $A$ is a $k$-term arithmetic progression. In this paper, we give some nontrivial inverse results of the sets $A$ with some extremal the cardinalities of $hA$. Keywords : Sumsets, inverse problem, arithmetic progression MSC numbers : 11B13 Supported by : This work was supported by the National Natural Science Foundation of China(Grant No. 11971033) and top talents project of Anhui Department of Education(Grant No. gxbjZD05) Downloads: Full-text PDF   Full-text HTML