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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2602.01252 |
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| _version_ | 1866908802834497536 |
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| author | Kominers, Scott Duke |
| author_facet | Kominers, Scott Duke |
| contents | Recently, Harrington, Litman, and Wong [Bulletin of the Australian Mathematical Society, 2024; arXiv:2303.06534] proved that every arithmetic progression contains infinitely many base-$b$ Niven numbers, for any fixed $b\ge 2$. We use a sparse repunit construction to treat a structured two-base version of the same problem, showing that every arithmetic progression with common difference relatively prime to $b$ contains infinitely many integers that are simultaneously $b$-Niven and $b^k$-Niven (indeed, we can obtain simultaneous $b^\ell$-Niven-ness for $\ell=1,\ldots, k$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01252 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simultaneous Niven Numbers in Arithmetic Progressions for Power-Related Bases Kominers, Scott Duke Number Theory 11A63, 11B25 Recently, Harrington, Litman, and Wong [Bulletin of the Australian Mathematical Society, 2024; arXiv:2303.06534] proved that every arithmetic progression contains infinitely many base-$b$ Niven numbers, for any fixed $b\ge 2$. We use a sparse repunit construction to treat a structured two-base version of the same problem, showing that every arithmetic progression with common difference relatively prime to $b$ contains infinitely many integers that are simultaneously $b$-Niven and $b^k$-Niven (indeed, we can obtain simultaneous $b^\ell$-Niven-ness for $\ell=1,\ldots, k$). |
| title | Simultaneous Niven Numbers in Arithmetic Progressions for Power-Related Bases |
| topic | Number Theory 11A63, 11B25 |
| url | https://arxiv.org/abs/2602.01252 |