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Mathematics of Computation

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Primitive values of quadratic polynomials in a finite field

Authors: Andrew R. Booker, Stephen D. Cohen, Nicole Sutherland and Tim Trudgian
Journal: Math. Comp. 88 (2019), 1903-1912
MSC (2010): Primary 11T30; Secondary 11Y16
Published electronically: October 30, 2018
MathSciNet review: 3925490
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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$.

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Additional Information

Andrew R. Booker
Affiliation: School of Mathematics, University of Bristol, Bristol, England

Stephen D. Cohen
Affiliation: School of Mathematics and Statistics, University of Glasgow, Glasgow, Scotland

Nicole Sutherland
Affiliation: Computational Algebra Group, School of Mathematics and Statistics, University of Sydney, Sydney, Australia

Tim Trudgian
Affiliation: School of Physical, Environmental and Mathematical Sciences, The University of New South Wales Canberra, Canberra, Australia

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.
Article copyright: © Copyright 2018 American Mathematical Society