Publication [4.14] of Tomás Oliveira e Silva

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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.


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

  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}