Primitive values of quadratic polynomials in a finite field
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- by Andrew R. Booker, Stephen D. Cohen, Nicole Sutherland and Tim Trudgian HTML | PDF
- Math. Comp. 88 (2019), 1903-1912 Request permission
Abstract:
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 $b^{2} - 4ac \neq 0$.References
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Additional Information
- Andrew R. Booker
- Affiliation: School of Mathematics, University of Bristol, Bristol, England
- MR Author ID: 672596
- Email: andrew.booker@bristol.ac.uk
- Stephen D. Cohen
- Affiliation: School of Mathematics and Statistics, University of Glasgow, Glasgow, Scotland
- MR Author ID: 50360
- Email: stephen.cohen@glasgow.ac.uk
- Nicole Sutherland
- Affiliation: Computational Algebra Group, School of Mathematics and Statistics, University of Sydney, Sydney, Australia
- MR Author ID: 975175
- Email: nicole.sutherland@sydney.edu.au
- Tim Trudgian
- Affiliation: School of Physical, Environmental and Mathematical Sciences, The University of New South Wales Canberra, Canberra, Australia
- MR Author ID: 909247
- Email: t.trudgian@adfa.edu.au
- Received by editor(s): March 4, 2018
- Received by editor(s) in revised form: March 22, 2018, and June 18, 2018
- Published electronically: October 30, 2018
- Additional Notes: The first author was partially supported by EPSRC Grant EP/K034383/1.
The fourth author was supported by Australian Research Council Future Fellowship FT160100094. - © Copyright 2018 American Mathematical Society
- Journal: Math. Comp. 88 (2019), 1903-1912
- MSC (2010): Primary 11T30; Secondary 11Y16
- DOI: https://doi.org/10.1090/mcom/3390
- MathSciNet review: 3925490