Covering systems with restricted divisibility

Robert D. Hough; Pace P. Nielsen

doi:10.1215/00127094-2019-0058

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15 November 2019 Covering systems with restricted divisibility

Robert D. Hough, Pace P. Nielsen

Abstract

We prove that every distinct covering system has a modulus divisible by either $2$ or $3$ .

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Robert D. Hough. Pace P. Nielsen. "Covering systems with restricted divisibility." Duke Math. J. 168 (17) 3261 - 3295, 15 November 2019. https://doi.org/10.1215/00127094-2019-0058

Information

Received: 13 March 2017; Revised: 10 April 2019; Published: 15 November 2019

First available in Project Euclid: 30 October 2019

zbMATH: 07154926

MathSciNet: MR4030365

Digital Object Identifier: 10.1215/00127094-2019-0058

Subjects:

Primary: 11A07

Secondary: 11B25 , 11K99

Keywords: covering system , Lovasz local lemma , odd covering problem , Shearer’s theorem

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