Finite addition theorems. I
type: Item
instance of: scholarly article
title: Finite addition theorems. I
zbMATH Open document ID: 0674.10042
DOI: 10.1016/0022-314X(89)90102-9
published in: Journal of Number Theory
publication date: 1989-01-01T00:00:00Z
review text: The author proves that, given natural numbers N, k and a set \(A\subseteq \{1,2,...,N\}\) with \(| A| \geq (N/k)+1\), there exist integers d,\(\ell,m\); \(1\leq d<k\); \(1\leq \ell <118k\), such that \(\ell A\) contains the arithmetic progression \(\{(m+i)d|\) \(i=1,...,N\}\). A second theorem shows that, roughly speaking, the factor 118 cannot be replaced by 1.
reviewed by: Bodo Volkmann
Mathematics Subject Classification ID: 11B13
Mathematics Subject Classification ID: 11B25
zbMATH DE Number: 4103201
zbMATH Keywords: addition of finite sets
zbMATH Keywords: Szemerédi's theorem
zbMATH Keywords: additive bases
zbMATH Keywords: arithmetic progression
author: András Sárközy
MaRDI profile type: Publication
cites work: A Theorem on the Densities of Sets of Integers
cites work: On the Representation of Integers as Sums of Distinct Terms from a Fixed Sequence
cites work: Q3963072
cites work: Abschätzung der asymptotischen Dichte von Summenmengen
cites work: A proof of the fundamental theorem on the density of sums of sets of positive integers
cites work: On sets of integers containing k elements in arithmetic progression
description: scientific article; zbMATH DE number 4103201