Skip to main content
Log in

Two-side estimates of the number of fixed points of a discrete logarithm

  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

Lower and upper bounds are obtained for an average number of solutions to the congruence g x x (mod p) in nonnegative integer numbers xp − 1, where g is a primitive root modulo p.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. K. Guy, Unsolved Problems in Number Theory, 2nd ed. (Springer-Verlag, New York, Berlin, 1994).

    MATH  Google Scholar 

  2. M. E. Campbell, On Fixed Points for Discrete Logarithms, Master’s thesis (Univ. California at Berkeley, 2003).

  3. S. V. Konyagin and I. E. Shparlinski, Character Sums with Exponential Functions and Their Applications (Cambridge Univ. Press, Cambridge, 1999).

    Book  MATH  Google Scholar 

  4. S. Ramanujan, “Highly Composite Numbers. Annotated and with a Foreword by Nicolas J.-L. and Robin G,” Ramanujan J. 1(2), 119 (1997).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © E.A. Grechnikov, 2012, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2012, Vol. 67, No. 3, pp. 3–8.

About this article

Cite this article

Grechnikov, E.A. Two-side estimates of the number of fixed points of a discrete logarithm. Moscow Univ. Math. Bull. 67, 91–96 (2012). https://doi.org/10.3103/S0027132212030011

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132212030011

Keywords

Navigation