Counting fixed points and rooted closed walks of the singular map $x\mapsto x^{x^n}$ modulo powers of a prime

Joshua Holden, Pamela A. Richardson, Margaret M. Robinson

The "self-power" map $x\mapsto x^x$ modulo $m$ and its generalized form $x\mapsto x^{x^n}$ modulo $m$ are of considerable interest for both theoretical reasons and for potential…