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A note on primitive roots in finite fields

Published online by Cambridge University Press:  26 February 2010

John B. Friedlander
John B. Friedlander
Affiliation:
The Pennsylvania State University.
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Extract

Let K be the finite field of pn elements, and Zp its prime subfield. It was proved by Davenport [3] that if p > p0(n) and θ is any given generating element of K, then there exists an integer m such that θ + m is a primitive root of K.

Type
Research Article
Information
Mathematika , Volume 19 , Issue 1 , June 1972 , pp. 112 - 114
Copyright
Copyright © University College London 1972

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References

1.Burgess, D. A., “The distribution of quadratic residues and non-residues”, Mathematika, 4 (1957), 106–112.CrossRefGoogle Scholar
2.Burgess, D. A., “On character sums and primitive roots, “Proc. London Math. Soc. (3), 12 (1962). 179–192.CrossRefGoogle Scholar
3.Davenport, H., “On primitive roots in finite fields”, Quart, J. Math. (Oxford), 8 (1937), 308–312.CrossRefGoogle Scholar
4.Davenport, H., and Lewis, D. J., “Character sums and primitive roots in finite fields”, Rend. Circ. Mat. Palermo, II, 12 (1963), 129–136.CrossRefGoogle Scholar