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

TL;DR

This paper proves that for all finite fields with size greater than 61, every non-zero element can be expressed as a linear combination of two primitive roots, confirming a conjecture by Cohen and Mullen.

Contribution

It provides a proof confirming the Cohen and Mullen conjecture for all finite fields with size greater than 61.

Findings

Every non-zero element in $_{q}$ can be written as a linear combination of two primitive roots for all $q>61$

The conjecture by Cohen and Mullen is fully resolved for large finite fields

The result advances understanding of primitive roots in finite fields

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.