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On consecutive primitive elements in a finite field
For an odd prime power with we prove that there are always three
consecutive primitive elements in the finite field . Indeed,
there are precisely eleven values of for which this is false. For
we present conjectures on the size of such that
guarantees the existence of consecutive primitive elements in
, provided that has characteristic at
least~. Finally, we improve the upper bound on for all .Comment: 10 pages, 2 table
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