On the cycle structure of repeated exponentiation modulo a prime
Repeated exponentiation modulo a prime is a simple but significant dynamical system defined over a finite field. The authors consider several observables, such as the total numer of cycles and the size of the maximal invariant set. Extending results of Shallit and Vasiga (who dealt with repeated squaring), the authors provide explicit formulae for such quantities. In addition, they establish the corresponding asymptotic (large prime) formulae, without assuming the validity of the Generalized Riemann Hypothesis.
scientific article; zbMATH DE number 2091716
scientific article