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Covering systems with the sum of the reciprocals of the moduli close to 1

Year: 2026

Type: article

Abstract: In 1952, H. Davenport posed the problem of determining a condition on the minimum modulus m 0 m_{0} in a finite distinct covering system that would imply that the sum of the reciprocals of the moduli in the covering system is bounded away from 1 1 . In 1973, P. Erdős and J. Selfridge indicated that they believed that m 0 > 4 m_{0} > 4 would suffice. We provide a proof that this is the case.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/tran/9670

Authors: Michael Filaseta, Alexandros Kalogirou

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7125585109

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Cites: 21

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