On the Fixed Points of the Map x -> x^x Modulo a Prime
Number Theory
2014-02-19 v1 Dynamical Systems
Abstract
In this paper, we show that for almost all primes p there is an integer solution x in [2,p-1] to the congruence x^x == x mod p. The solutions can be interpretated as fixed points of the map x -> x^x mod p, and we study numerically and discuss some unexpected properties of the dynamical system associated with this map.
Cite
@article{arxiv.1402.4464,
title = {On the Fixed Points of the Map x -> x^x Modulo a Prime},
author = {Pär Kurlberg and Florian Luca and Igor Shparlinski},
journal= {arXiv preprint arXiv:1402.4464},
year = {2014}
}
Comments
25 pages