On a sumset problem for integers
type: Item
instance of: scholarly article
title: On a sumset problem for integers
zbMATH Open document ID: 1308.11010
author: Shan-Shan Du
author: Hui-Qin Cao
author: Zhi-Wei Sun
published in: The Electronic Journal of Combinatorics
publication date: 2014-09-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1011.5438
full work available at URL: v21i1p13
review text: Summary: Let \(A\) be a finite set of integers. We show that if \(k\) is a prime power or a product of two distinct primes then \[ |A+k\cdot A|\geq(k+1)|A|-\lceil k(k+2)/4\rceil \] provided \(|A|\geq (k-1)^{2}k!\), where \(A+k\cdot A=\{a+kb:\;a,b\in A\}\). We also establish the inequality \(|A+4\cdot A|\geq5|A|-6 \) for \(|A|\geq5\).
Mathematics Subject Classification ID: 11B30
Mathematics Subject Classification ID: 11B13
Mathematics Subject Classification ID: 05E99
Mathematics Subject Classification ID: 11P70
zbMATH DE Number: 6340111
zbMATH Keywords: additive combinatorics
zbMATH Keywords: sumsets
MaRDI profile type: Publication
arXiv ID: 1011.5438
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description: scientific article; zbMATH DE number 6340111