On a problem of Erdős on integers, none of which divides the product of \(k\) others
type: Item
instance of: scholarly article
title: On a problem of Erdős on integers, none of which divides the product of \(k\) others
zbMATH Open document ID: 1255.11008
author: Tsz Ho Chan
author: András Sárközy
author: Ervin Győri
published in: European Journal of Combinatorics
publication date: 2009-12-01T00:00:00Z
review text: Let \(F_{k}(N)\) denote the maximal number of integers selected from \(\{1, \dots, N\}\), so that none of them divides the product of \(k\) others. Following Erdős's approach for \(k = 2\), the authors give a lower estimation to \(F_{k}(N)\) for \(2 \leq k \leq \frac{\log N}{6\log \log N}\). They give an upper bound for \(F_{3}(N)\) and also prove that the lower bound for \(F_{3}(N)\) is sharp apart from a constant factor. The proofs use combinatorial arguments and some elementary number theory.
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 05D05
Mathematics Subject Classification ID: 05C90
zbMATH DE Number: 5641333
zbMATH Keywords: multiplicative Sidon set
zbMATH Keywords: primitive set
reviewed by: Sándor Kiss
MaRDI profile type: Publication
full work available at URL: j.ejc.2009.02.005
OpenAlex ID: W2064183481
cites work: On the density of primitive sets
cites work: Q5608848
cites work: Families of finite sets in which no set is covered by the union of \(r\) others
cites work: On product representation of powers. I
cites work: Q5614074
cites work: \(C_ 6\)-free bipartite graphs and product representation of squares
cites work: An extremal problem for paths in bipartite graphs
cites work: The Existence and Construction of Balanced Incomplete Block Designs
cites work: Q2785586
DOI: 10.1016/J.EJC.2009.02.005
description: scientific article; zbMATH DE number 5641333