Addenda/Corrigenda: Fixed Points and Two-cycles of the Discrete Logarithm
Abstract
Description
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.
6 pages. This report consists of additions and corrections to the Author's paper (http://link.springer-ny.com/link/service/series/0558/bibs/2369/23690405.htm) which appeared in the proceedings of the ANTS V conference. The work described here was presented at the conference itself, which took place after the original paper was published. Version 2: more typos in the original found and corrected
6 pages. This report consists of additions and corrections to the Author's paper (http://link.springer-ny.com/link/service/series/0558/bibs/2369/23690405.htm) which appeared in the proceedings of the ANTS V conference. The work described here was presented at the conference itself, which took place after the original paper was published. Version 2: more typos in the original found and corrected