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

Cohen, Stephen; Oliveira e Silva, Tomás; Trudgian, Tim

doi:10.1090/mcom/2950

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.

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