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Primitive values of quadratic polynomials in a finite field (1803.01435v2)
Published 4 Mar 2018 in math.NT
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 $Q(x)= ax2 + bx + c$ is a quadratic polynomial with $a, b, c\in \mathbb{F}{q}$ such that $b{2} - 4ac \neq 0$.