Hybrid bounds for prime divisors
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917852765749248 |
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| author | Bagger, Gustav Kjærbye |
| author_facet | Bagger, Gustav Kjærbye |
| contents | Let $x$ and $n$ be positive integers. We prove a non-trivial lower bound for $x$, dependant only on $ω_n$, the number of distinct prime factors of $x^n-1$. By considering the divisibility of $φ\mid x^n-1$ for $φ\mid n$, we obtain a further refinement. This bound has applications for existence problems relating to primitive elements in finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00010 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hybrid bounds for prime divisors Bagger, Gustav Kjærbye Number Theory 11A07, 11T22 Let $x$ and $n$ be positive integers. We prove a non-trivial lower bound for $x$, dependant only on $ω_n$, the number of distinct prime factors of $x^n-1$. By considering the divisibility of $φ\mid x^n-1$ for $φ\mid n$, we obtain a further refinement. This bound has applications for existence problems relating to primitive elements in finite fields. |
| title | Hybrid bounds for prime divisors |
| topic | Number Theory 11A07, 11T22 |
| url | https://arxiv.org/abs/2412.00010 |