On the intervals for the non-existence of covering systems with distinct moduli
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915340772966400 |
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| author | Dalton, Jack Jones, Nic |
| author_facet | Dalton, Jack Jones, Nic |
| contents | In a research seminar in $2006$, M. Filaseta, O. Trifonov, and G. Yu showed for each integer $n\geq3$ there is no distinct covering with all moduli in the interval $[n, 6n]$. In $2022$, this interval was subsequently improved to $[n, 8n]$ by the first author and O. Trifonov. The first author then improved this bound to $[n, 9n]$ in $2023$. Building off their method, we show that for each integer $n\geq 3$, there does not exist a distinct covering system with all moduli in the interval $[n, 10n]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11359 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the intervals for the non-existence of covering systems with distinct moduli Dalton, Jack Jones, Nic Number Theory In a research seminar in $2006$, M. Filaseta, O. Trifonov, and G. Yu showed for each integer $n\geq3$ there is no distinct covering with all moduli in the interval $[n, 6n]$. In $2022$, this interval was subsequently improved to $[n, 8n]$ by the first author and O. Trifonov. The first author then improved this bound to $[n, 9n]$ in $2023$. Building off their method, we show that for each integer $n\geq 3$, there does not exist a distinct covering system with all moduli in the interval $[n, 10n]$. |
| title | On the intervals for the non-existence of covering systems with distinct moduli |
| topic | Number Theory |
| url | https://arxiv.org/abs/2506.11359 |