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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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Publisher copy:
10.2140/ant.2021.15.609

Authors

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Wadham College
Role:
Author
ORCID:
0000-0003-2696-0352
Publisher:
Mathematical Sciences Publishers Publisher's website
Journal:
Algebra & Number Theory Journal website
Volume:
15
Issue:
3
Pages:
609–626
Publication date:
2021-05-20
Acceptance date:
2020-09-18
DOI:
EISSN:
1944-7833
ISSN:
1937-0652
Language:
English
Keywords:
Pubs id:
1131646
Local pid:
pubs:1131646
Deposit date:
2020-09-20

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