Primitive values of quadratic polynomials in a finite field
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2018
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| _version_ | 1866929225040134144 |
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| author | Booker, Andrew R. Cohen, Stephen D. Sutherland, Nicole Trudgian, Tim |
| author_facet | Booker, Andrew R. Cohen, Stephen D. Sutherland, Nicole Trudgian, Tim |
| contents | We prove that for all $q>211$, there always exists a primitive root $g$ in the finite field $\mathbb{F}_{q}$ such that $Q(g)$ is also a primitive root, where $Q(x)= ax^2 + bx + c$ is a quadratic polynomial with $a, b, c\in \mathbb{F}_{q}$ such that $b^{2} - 4ac \neq 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_01435 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Primitive values of quadratic polynomials in a finite field Booker, Andrew R. Cohen, Stephen D. Sutherland, Nicole Trudgian, Tim Number Theory 11T30, 11Y16 We prove that for all $q>211$, there always exists a primitive root $g$ in the finite field $\mathbb{F}_{q}$ such that $Q(g)$ is also a primitive root, where $Q(x)= ax^2 + bx + c$ is a quadratic polynomial with $a, b, c\in \mathbb{F}_{q}$ such that $b^{2} - 4ac \neq 0$. |
| title | Primitive values of quadratic polynomials in a finite field |
| topic | Number Theory 11T30, 11Y16 |
| url | https://arxiv.org/abs/1803.01435 |