Title

Fixed Points and Two-Cycles of the Discrete Logarithm

Document Type

Article

Publication Date

2002

Abstract

We explore some questions related to one of Brizolis: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? We extend this question to ask about not only fixed points but also two-cycles. Campbell and Pomerance have not only answered the fixed point question for sufficiently large p but have also rigorously estimated the number of such pairs given certain conditions on g and h. We attempt to give heuristics for similar estimates given other conditions on g and h and also in the case of two-cycles. These heuristics are well-supported by the data we have collected, and seem suitable for conversion into rigorous estimates in the future.

DOI Number

10.1007/3-540-45455-1_32

External Access URL

https://doi.org/10.1007/3-540-45455-1_32

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