Vol. 15, No. 3, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18, 1 issue

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
The Erdős–Selfridge problem with square-free moduli

Paul Balister, Béla Bollobás, Robert Morris, Julian Sahasrabudhe and Marius Tiba

Vol. 15 (2021), No. 3, 609–626

A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of covering systems with distinct moduli was initiated by Erdős in 1950, and over the following decades numerous problems were posed regarding their properties. One particularly notorious question, due to Erdős, asks whether there exist covering systems whose moduli are distinct and all odd. We show that if in addition one assumes the moduli are square-free, then there must be an even modulus.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

covering systems, Erdős–Selfridge problem
Mathematical Subject Classification 2010
Primary: 11B25
Secondary: 11A07, 11N35
Received: 31 January 2019
Revised: 14 August 2020
Accepted: 18 September 2020
Published: 20 May 2021
Paul Balister
University of Oxford
United Kingdom
Béla Bollobás
University of Cambridge
United Kingdom
University of Memphis
Memphis, TN
United States
Robert Morris
Rio de Janeiro
Julian Sahasrabudhe
University of Cambridge
United Kingdom
Marius Tiba
University of Cambridge
United Kingdom