On the Sum of a Prime and a Number that is not Square-Free
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913085844881408 |
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| author | Lee, Ethan S. O'Clarey, Rowan |
| author_facet | Lee, Ethan S. O'Clarey, Rowan |
| contents | We prove that every sufficiently large integer $n$ can be written as the sum of a prime and an integer that is not square-free. In addition, we expect this result holds for every $n > 24$ and prove two results to support this claim. First, we prove the result holds unconditionally for every odd $n > 24$. Second, assuming the Generalised Riemann Hypothesis for Dirichlet $L$-functions, we prove the result holds for every $n > 24$. We also discuss the obstruction which prohibits us from proving the result unconditionally for every $n > 24$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02426 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Sum of a Prime and a Number that is not Square-Free Lee, Ethan S. O'Clarey, Rowan Number Theory 11P32, 11A07, 11Y35 We prove that every sufficiently large integer $n$ can be written as the sum of a prime and an integer that is not square-free. In addition, we expect this result holds for every $n > 24$ and prove two results to support this claim. First, we prove the result holds unconditionally for every odd $n > 24$. Second, assuming the Generalised Riemann Hypothesis for Dirichlet $L$-functions, we prove the result holds for every $n > 24$. We also discuss the obstruction which prohibits us from proving the result unconditionally for every $n > 24$. |
| title | On the Sum of a Prime and a Number that is not Square-Free |
| topic | Number Theory 11P32, 11A07, 11Y35 |
| url | https://arxiv.org/abs/2605.02426 |