## Consecutive primitive roots in a finite field

HTML articles powered by AMS MathViewer

- by Stephen D. Cohen PDF
- Proc. Amer. Math. Soc.
**93**(1985), 189-197 Request permission

## Abstract:

Every finite field of order $q( > 3)$ such that $q \not \equiv 7(\mod 12)$ and $q \not \equiv 1(\mod 60)$ contains a pair of consecutive primitive roots.## References

- L. Carlitz,
*Distribution of primitive roots in a finite field*, Quart. J. Math. Oxford Ser. (2)**4**(1953), 4–10. MR**56028**, DOI 10.1093/qmath/4.1.4 - L. Carlitz,
*Sets of primitive roots*, Compositio Math.**13**(1956), 65–70. MR**83002** - Stephen D. Cohen,
*Primitive roots in the quadratic extension of a finite field*, J. London Math. Soc. (2)**27**(1983), no. 2, 221–228. MR**692527**, DOI 10.1112/jlms/s2-27.2.221 - Kenneth F. Ireland and Michael I. Rosen,
*A classical introduction to modern number theory*, Graduate Texts in Mathematics, vol. 84, Springer-Verlag, New York-Berlin, 1982. Revised edition of*Elements of number theory*. MR**661047** - Emanuel Vegh,
*Pairs of consecutive primitive roots modulo a prime*, Proc. Amer. Math. Soc.**19**(1968), 1169–1170. MR**230680**, DOI 10.1090/S0002-9939-1968-0230680-7 - Emanuel Vegh,
*A note on the distribution of the primitive roots of a prime*, J. Number Theory**3**(1971), 13–18. MR**285476**, DOI 10.1016/0022-314X(71)90046-1

## Additional Information

- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**93**(1985), 189-197 - MSC: Primary 11T30; Secondary 11N69
- DOI: https://doi.org/10.1090/S0002-9939-1985-0770516-9
- MathSciNet review: 770516