Covering systems with the sum of the reciprocals of the moduli close to $1$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916331557748736 |
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| author | Filaseta, Michael Kalogirou, Alexandros |
| author_facet | Filaseta, Michael Kalogirou, Alexandros |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Covering systems with the sum of the reciprocals of the moduli close to $1$ Filaseta, Michael Kalogirou, Alexandros Number Theory 11B25 (Primary) 11A07, 11B05 (Secondary) 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. |
| title | Covering systems with the sum of the reciprocals of the moduli close to $1$ |
| topic | Number Theory 11B25 (Primary) 11A07, 11B05 (Secondary) |
| url | https://arxiv.org/abs/2407.15280 |