On the sum of a prime and a square-free number co-prime to any integer with at most two prime factors
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911551696404480 |
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| author | Lee, Ethan S. O'Clarey, Rowan |
| author_facet | Lee, Ethan S. O'Clarey, Rowan |
| contents | Every natural number greater than $2$ can be written as the sum of a prime and a square-free number, and recent work has imposed additional divisibility conditions on the square-free number. We overcome limitations in these works to prove new results on square-free numbers co-prime to any integer with up to two prime factors, which make the expected asymptotic results explicit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11814 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the sum of a prime and a square-free number co-prime to any integer with at most two prime factors Lee, Ethan S. O'Clarey, Rowan Number Theory 11P32, 11A07, 11Y35 Every natural number greater than $2$ can be written as the sum of a prime and a square-free number, and recent work has imposed additional divisibility conditions on the square-free number. We overcome limitations in these works to prove new results on square-free numbers co-prime to any integer with up to two prime factors, which make the expected asymptotic results explicit. |
| title | On the sum of a prime and a square-free number co-prime to any integer with at most two prime factors |
| topic | Number Theory 11P32, 11A07, 11Y35 |
| url | https://arxiv.org/abs/2506.11814 |