On the Erdős-Straus non-averaging set problem
type: Item
instance of: scholarly article
title: On the Erdős-Straus non-averaging set problem
zbMATH Open document ID: 0607.10039
DOI: 10.1007/BF01949131
author: H. L. Abbott
published in: Acta Mathematica Hungarica
publication date: 1986-01-01T00:00:00Z
review text: A set \(S\) of integers is said to be non-averaging if the arithmetic mean of two or more elements of \(S\) does not belong to \(S\). Let \(f(n)\) denote the cardinality of a largest non-averaging subset of \(\{0,1,\ldots,n\}\). The problem of Erdős-Straus is to give upper and lower bounds for \(f(n)\). This paper contains an improvement upon results of E. G. Straus and the author, showing that \(f(n)\gg n^{1/5}\) for all sufficiently large \(n\) and \(f(n)\gg n^{1/5}(\log \log n)^{2/5}\) for infinitely many \(n\).
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 3981282
zbMATH Keywords: cardinality
zbMATH Keywords: largest non-averaging subset
zbMATH Keywords: problem of Erdős-Straus
reviewed by: A. Perelli
MaRDI profile type: Publication
cites work: Extremal problems on non-averaging and non-dividing sets
cites work: On non-averaging sets of integers
cites work: On Sets of Integers Which Contain No Three Terms in Arithmetical Progression
cites work: Q3259107
full work available at URL: https://doi.org/10.1007/bf01949131
OpenAlex ID: W2044817124
description: scientific article; zbMATH DE number 3981282