Small Prime Primitive Roots in Arithmetic Progressions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915509607333888 |
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| author | Carella, N. A. |
| author_facet | Carella, N. A. |
| contents | Let $p>1$ be a large prime number, let $q=O(\log\log p)$ and let $1\leq a<q$ be a pair of relatively prime integers. It is proved that there is a prime primitive root $u\ll (\log p)(\log \log p)^5$ such that $u\equiv a\bmod q$ in the prime finite field $\mathbb{F}_p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Small Prime Primitive Roots in Arithmetic Progressions Carella, N. A. General Mathematics Primary 11A07, 11N05, Secondary 11N32 Let $p>1$ be a large prime number, let $q=O(\log\log p)$ and let $1\leq a<q$ be a pair of relatively prime integers. It is proved that there is a prime primitive root $u\ll (\log p)(\log \log p)^5$ such that $u\equiv a\bmod q$ in the prime finite field $\mathbb{F}_p$. |
| title | Small Prime Primitive Roots in Arithmetic Progressions |
| topic | General Mathematics Primary 11A07, 11N05, Secondary 11N32 |
| url | https://arxiv.org/abs/2509.19309 |