A proof of the conjecture of Cohen and Mullen on sums of primitive roots
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- by Stephen D. Cohen, Tomás Oliveira e Silva and Tim Trudgian PDF
- Math. Comp. 84 (2015), 2979-2986 Request permission
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.References
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Additional Information
- Stephen D. Cohen
- Affiliation: School of Mathematics and Statistics, University of Glasgow, Scotland
- MR Author ID: 50360
- Email: Stephen.Cohen@glasgow.ac.uk
- Tomás Oliveira e Silva
- Affiliation: Departamento de Electrónica, Telecomunicações e Informática/IEETA, Universidade de Aveiro, Portugal
- ORCID: 0000-0002-8878-3219
- Email: tos@ua.pt
- Tim Trudgian
- Affiliation: Mathematical Sciences Institute, The Australian National University, ACT 2601, Australia
- MR Author ID: 909247
- Email: timothy.trudgian@anu.edu.au
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp. 84 (2015), 2979-2986
- MSC (2010): Primary 11T30, 11Y99
- DOI: https://doi.org/10.1090/mcom/2950
- MathSciNet review: 3378858