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arXiv · 2407.15280

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

Michael Filaseta·Alexandros Kalogirou
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Abstract

In 1952, H. Davenport posed the problem of determining a condition on the minimum modulus $m_{0}$ 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 $1$. In 1973, P. Erdos and J. Selfridge indicated that they believed that $m_{0} > 4$ would suffice. We provide a proof that this is the case.

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Michael Filaseta, Alexandros Kalogirou. 2024-07-21. Covering systems with the sum of the reciprocals of the moduli close to $1$. https://arxiv.org/abs/2407.15280

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