# Publication [4.14] of Tomás Oliveira e Silva

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## 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} }