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.Comment: 8 pages; to appear in Mathematics of Computatio