Niven numbers are an asymptotic basis of order 3
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918186376495104 |
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| author | Thomas, Kate |
| author_facet | Thomas, Kate |
| contents | A base-$g$ Niven number is a natural number divisible by the sum of its base-$g$ digits. We show that, for any $g\geq 3$, all sufficiently large natural numbers can be written as the sum of three base-$g$ Niven numbers. We also give an asymptotic formula for the number of representations of a sufficiently large integer as the sum of three integers with fixed, close to average, digit sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Niven numbers are an asymptotic basis of order 3 Thomas, Kate Number Theory A base-$g$ Niven number is a natural number divisible by the sum of its base-$g$ digits. We show that, for any $g\geq 3$, all sufficiently large natural numbers can be written as the sum of three base-$g$ Niven numbers. We also give an asymptotic formula for the number of representations of a sufficiently large integer as the sum of three integers with fixed, close to average, digit sums. |
| title | Niven numbers are an asymptotic basis of order 3 |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.02790 |