# Publication [4.14] of Tomás Oliveira e Silva

Do not bookmark this page, because its URI may change in the future.
Instead, bookmark its parent page (http://sweet.ua.pt/tos/bib.html).

## Reference

Stephen D. Cohen, Tomás Oliveira e Silva and Tim Trudgian, "On Consecutive Primitive Elements in a Finite Field," Bulletin of the London Mathematical Society, vol. 47, pp. 418-426, 2015.

## Abstract

For q an odd prime power with q>169 we prove that there are always three consecutive primitive elements in the finite field F_q. Indeed, there are precisely eleven values of q>169 for which this is false. For 4\leq n\leq 8 we present conjectures on the size of q_0(n) such that q>q_0(n) guarantees the existence of n consecutive primitive elements in F_q, provided that F_q has characteristic at least n. Finally, we improve the upper bound on q_0(n) for all n\geq 3.

## BibTeX entry

@Article
{
Cohen-2015-3-COEFF,
author = {Cohen, Stephen D.} # { and } # {Oliveira e Silva, Tom{\'a}s} #
{ and } # {Trudgian, Tim},
title = {On Consecutive Primitive Elements in a Finite Field},
journal = {Bulletin of the {L}ondon Mathematical Society},
year = {2015},
volume = {47},
pages = {418--426}
}