A proof of the conjecture of Cohen and Mullen on sums of primitive roots

Abstract

We prove that for all $q>61$, every non-zero element in the finite field ${\mathbb{F}}_q$ can be written as a linear combination of two primitive roots of ${\mathbb{F}}_q$. This resolves a conjecture posed by Cohen and Mullen.

8 pages; to appear in Mathematics of Computation