Existence results for primitive elements in cubic and quartic extensions of a finite field

Geoff Bailey, Stephen D. Cohen, Nicole Sutherland +1

With $\Fq$ the finite field of $q$ elements, we investigate the following question. If $\gamma$ generates $\Fqn$ over $\Fq$ and $\beta$ is a non-zero element of $\Fqn$, is there always an $…