Statistics for fixed points of the self-power map

Matthew Friedrichsen, Joshua Holden
2019 Involve. A Journal of Mathematics  
The map x -> x^x modulo p is related to a variation of the digital signature scheme in a similar way to the discrete exponentiation map, but it has received much less study. We explore the number of fixed points of this map by a statistical analysis of experimental data. In particular, the number of fixed points can in many cases be modeled by a binomial distribution. We discuss the many cases where this has been successful, and also the cases where a good model may not yet have been found.
doi:10.2140/involve.2019.12.63 fatcat:ybfudyq42nbxtjjgjzl32jvfza