A further investigation on covering systems with odd moduli
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913078499606528 |
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| author | Bispels, Chris Cohen, Matthew Harrington, Joshua Lowrance, Joshua Pontes, Kaelyn Schaumann, Leif Wong, Tony W. H. |
| author_facet | Bispels, Chris Cohen, Matthew Harrington, Joshua Lowrance, Joshua Pontes, Kaelyn Schaumann, Leif Wong, Tony W. H. |
| contents | Erdős first introduced the idea of covering systems in 1950. Since then, much of the work in this area has concentrated on identifying covering systems that meet specific conditions on their moduli. Among the central open problems in this field is the well-known odd covering problem. In this paper, we investigate a variant of that problem, where one odd integer is permitted to appear multiple times as a modulus in the covering system, while all remaining moduli are distinct odd integers greater than 1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16135 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A further investigation on covering systems with odd moduli Bispels, Chris Cohen, Matthew Harrington, Joshua Lowrance, Joshua Pontes, Kaelyn Schaumann, Leif Wong, Tony W. H. Number Theory 11A07 Erdős first introduced the idea of covering systems in 1950. Since then, much of the work in this area has concentrated on identifying covering systems that meet specific conditions on their moduli. Among the central open problems in this field is the well-known odd covering problem. In this paper, we investigate a variant of that problem, where one odd integer is permitted to appear multiple times as a modulus in the covering system, while all remaining moduli are distinct odd integers greater than 1. |
| title | A further investigation on covering systems with odd moduli |
| topic | Number Theory 11A07 |
| url | https://arxiv.org/abs/2507.16135 |