Addenda/Corrigenda: Fixed Points and Two-cycles of the Discrete Logarithm

Details Addenda/Corrigenda: Fixed Points and Two-cycles of the Discrete Logarithm Addenda/Corrigenda: Fixed Points and Two-cycles of the Discrete Logarithm

2002-08-04

arxiv.org/abs/math/0208028v2

Mathematics

Number Theory

6 pages. This report consists of additions and corrections to the Author's paper (http://link.springer-ny.com/link/service/s

Scientific paper

The abstract of the original paper was as follows: 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.

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