Primitive element pairs with a prescribed trace in the cubic extension of a finite field

Andrew R. Booker, Stephen D. Cohen, Nicol Leong +1

We prove that for any prime power $q\notin \{3,4,5\}$, the cubic extension ${\mathbb{F}}_{q^3}$ of the finite field ${\mathbb{F}}_q$ contains a primitive element $\xi$ such that $ξ+ξ^{-1}…