Least Consecutive Pair of Primitive Roots
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910129959469056 |
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| author | Carella, N. A. |
| author_facet | Carella, N. A. |
| contents | Let $p>1$ be a large prime number and let $x=O((\log p)^2(\log\log p)^5$ be a real number. It is proved that the least consecutive pair of primitive roots $u\ne\pm1, v^2$ and $u+1$ satisfies the upper bound $u\ll x$ in the prime field $\mathbb{F}_p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13090 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Least Consecutive Pair of Primitive Roots Carella, N. A. General Mathematics Primary 11A07, 11N05, Secondary 11N32 Let $p>1$ be a large prime number and let $x=O((\log p)^2(\log\log p)^5$ be a real number. It is proved that the least consecutive pair of primitive roots $u\ne\pm1, v^2$ and $u+1$ satisfies the upper bound $u\ll x$ in the prime field $\mathbb{F}_p$. |
| title | Least Consecutive Pair of Primitive Roots |
| topic | General Mathematics Primary 11A07, 11N05, Secondary 11N32 |
| url | https://arxiv.org/abs/2604.13090 |