Bull. Korean Math. Soc. 2021; 58(2): 305-313
Online first article March 5, 2021 Printed March 31, 2021
https://doi.org/10.4134/BKMS.b200054
Copyright © The Korean Mathematical Society.
Min Tang, Yun Xing
Anhui Normal University; Anhui Normal University
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)
2015; 52(5): 1495-1515
1999; 36(4): 779-797
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