Journal article

The Erdős–Selfridge problem with square-free moduli

Abstract:: 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.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Balister, P., Bollobás, B., Morris, R., Sahasrabudhe, J., & Tiba, M. (2021). The Erdős–Selfridge problem with square-free moduli. Algebra & Number Theory, 15(3), 609–626.

MLA Style

Balister, P, et al. “The Erdős–Selfridge Problem with Square-Free Moduli.” Algebra & Number Theory, vol. 15, no. 3, 2021, pp. 609–26.

Chicago Style

Balister, P, B Bollobás, R Morris, J Sahasrabudhe, and M Tiba. 2021. “The Erdős–Selfridge Problem with Square-Free Moduli.” Algebra & Number Theory 15 (3): 609–26.
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Files:: ant-v15-n3-p02-s.pdf

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Publisher copy:: 10.2140/ant.2021.15.609

Authors

+ Balister, P More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Oxford college:: Wadham College
Role:: Author
ORCID:: 0000-0003-2696-0352

+ Bollobás, B More by this author

Role:: Author

+ Morris, R More by this author

Role:: Author

+ Sahasrabudhe, J More by this author

Role:: Author

+ Tiba, M More by this author

Role:: Author

Publisher:: Mathematical Sciences Publishers
Journal:: Algebra & Number Theory More from this journal
Volume:: 15
Issue:: 3
Pages:: 609–626
Publication date:: 2021-05-20
Acceptance date:: 2020-09-18
DOI:: 10.2140/ant.2021.15.609
EISSN:: 1944-7833
ISSN:: 1937-0652

Language:: English
Keywords:: FFR

Erdős–Selfridge problem

covering systems
Pubs id:: 1131646
Local pid:: pubs:1131646
Deposit date:: 2020-09-20
ARK identifier:: ark:/29072/ora_3c55267c60be465289a7db3db5f62c25

Terms of use

Copyright holder:: Mathematical Sciences Publishers
Copyright date:: 2021
Rights statement:: © Copyright 2021 Mathematical Sciences Publishers. All rights reserved.

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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