A polynomial with a root mod $p$ for every $p$ has a real root
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914842619674624 |
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| author | Angelo, Rodrigo Xu, Max Wenqiang |
| author_facet | Angelo, Rodrigo Xu, Max Wenqiang |
| contents | We prove that if a polynomial has a root mod $p$ for every large prime $p$, then it has a real root. As an application, we show that the primes can't be covered by finitely many positive definite binary quadratic forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13735 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A polynomial with a root mod $p$ for every $p$ has a real root Angelo, Rodrigo Xu, Max Wenqiang Number Theory We prove that if a polynomial has a root mod $p$ for every large prime $p$, then it has a real root. As an application, we show that the primes can't be covered by finitely many positive definite binary quadratic forms. |
| title | A polynomial with a root mod $p$ for every $p$ has a real root |
| topic | Number Theory |
| url | https://arxiv.org/abs/2210.13735 |