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

Stephen D. Cohen; Tomás Oliveira E. Silva; Tim Trudgian

doi:10.1090/mcom/2950

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

Stephen D. Cohen
, Tomás Oliveira E. Silva
, Tim Trudgian

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	2979-2986
Number of pages	8
Journal	Mathematics of Computation
Volume	84
Issue number	296
DOIs	https://doi.org/10.1090/mcom/2950
Publication status	Published - 2015

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title = "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 Fq can be written as a linear combination of two primitive roots of Fq. This resolves a conjecture posed by Cohen and Mullen.",

keywords = "Finite fields, Primitive roots",

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AU - Silva, Tomás Oliveira E.

AU - Trudgian, Tim

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N2 - We prove that for all q > 61, every non-zero element in the finite field Fq can be written as a linear combination of two primitive roots of Fq. This resolves a conjecture posed by Cohen and Mullen.

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

KW - Finite fields

KW - Primitive roots

UR - https://www.scopus.com/pages/publications/85000351017

U2 - 10.1090/mcom/2950

DO - 10.1090/mcom/2950

M3 - Article

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VL - 84

SP - 2979

EP - 2986

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 296

ER -

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

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