On the length of an interval that contains distinct multiples of the first $n$ positive integers
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911394154151936 |
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| author | van Doorn, Wouter |
| author_facet | van Doorn, Wouter |
| contents | Confirming a conjecture by Erd\H os and Pomerance, we prove that there exist intervals of length $\frac{cn\log n}{\log \log n}$ that do not contain distinct multiples of $1, 2, \ldots, n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16972 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the length of an interval that contains distinct multiples of the first $n$ positive integers van Doorn, Wouter Number Theory Confirming a conjecture by Erd\H os and Pomerance, we prove that there exist intervals of length $\frac{cn\log n}{\log \log n}$ that do not contain distinct multiples of $1, 2, \ldots, n$. |
| title | On the length of an interval that contains distinct multiples of the first $n$ positive integers |
| topic | Number Theory |
| url | https://arxiv.org/abs/2601.16972 |