Primitive values of quadratic polynomials in a finite field
Andrew R. Booker, Stephen D. Cohen, Nicole Sutherland, Tim Trudgian · Mathematics of Computation · 2018
We prove that for all q > 211 q>211 , there always exists a primitive root g g in the finite field F q \mathbb {F}_{q} such that Q ( g ) Q(g) is also a primitive root, where Q ( x ) = a x 2 + b x + c Q(x)= ax^2 + bx + c is a quadratic polynomial with a , b , c ∈ F q a, b, c\in \mathbb {F}_{q} such that b 2 − 4 a c ≠ 0 b^{2} - 4ac eq 0 .