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arXiv · 1803.01435

Primitive values of quadratic polynomials in a finite field

Andrew R. Booker·Stephen D. Cohen·Nicole Sutherland·Tim Trudgian
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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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Andrew R. Booker, Stephen D. Cohen, Nicole Sutherland, Tim Trudgian. 2018-03-22. Primitive values of quadratic polynomials in a finite field. https://doi.org/10.1090/mcom%2F3390

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