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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.09060 |
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| _version_ | 1866910697284173824 |
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| author | Filaseta, Michael Luca, Florian |
| author_facet | Filaseta, Michael Luca, Florian |
| contents | We show that if $n\ge n_0$, $b\ge 2$ are integers, $p\ge 7$ is prime and $n!-(b^p-1)/(b-1)\ge 0$, then $n!-(b^p-1)/(b-1) \ge 0.5\log\log n/\log\log\log n$. Further results are obtained, in particular for the case $n!-(b^p-1)/(b-1) < 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09060 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the distance between factorials and repunits Filaseta, Michael Luca, Florian Number Theory 11D61 We show that if $n\ge n_0$, $b\ge 2$ are integers, $p\ge 7$ is prime and $n!-(b^p-1)/(b-1)\ge 0$, then $n!-(b^p-1)/(b-1) \ge 0.5\log\log n/\log\log\log n$. Further results are obtained, in particular for the case $n!-(b^p-1)/(b-1) < 0$. |
| title | On the distance between factorials and repunits |
| topic | Number Theory 11D61 |
| url | https://arxiv.org/abs/2411.09060 |