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

Authors: Stephen D. Cohen, Tomás Oliveira e Silva and Tim Trudgian
Journal: Math. Comp. 84 (2015), 2979-2986
MSC (2010): Primary 11T30, 11Y99
Published electronically: March 30, 2015
MathSciNet review: 3378858
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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.

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Stephen D. Cohen
Affiliation: School of Mathematics and Statistics, University of Glasgow, Scotland

Tomás Oliveira e Silva
Affiliation: Departamento de Electrónica, Telecomunicações e Informática/IEETA, Universidade de Aveiro, Portugal

Tim Trudgian
Affiliation: Mathematical Sciences Institute, The Australian National University, ACT 2601, Australia

Keywords: Finite fields, primitive roots
Received by editor(s): February 11, 2014
Published electronically: March 30, 2015
Additional Notes: This work was supported by Australian Research Council DECRA Grant DE120100173
Article copyright: © Copyright 2015 American Mathematical Society