Document Type
Article
Publication Date
10-20-2002
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.
Recommended Citation
Holden, Joshua, "Fixed Point and Two-cycles of the Discrete Logarithm" (2002). Mathematical Sciences Technical Reports (MSTR). 93.
https://scholar.rose-hulman.edu/math_mstr/93
Included in
Applied Mathematics Commons, Discrete Mathematics and Combinatorics Commons, Number Theory Commons
Comments
MSTR 02-12