On the cycle structure of repeated exponentiation modulo a prime
type: Item
instance of: scholarly article
title: On the cycle structure of repeated exponentiation modulo a prime
zbMATH Open document ID: 1060.11059
author: Wun-Seng Chou
author: Igor E. Shparlinski
published in: Journal of Number Theory
publication date: 2004-08-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11N56
Mathematics Subject Classification ID: 11A15
zbMATH DE Number: 2091716
zbMATH Keywords: repeated powering
zbMATH Keywords: cycle structure
zbMATH Keywords: primes in arithmetic progressions
reviewed by: Franco Vivaldi
MaRDI profile type: Publication
full work available at URL: j.jnt.2004.04.005
OpenAlex ID: W2041524352
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DOI: 10.1016/J.JNT.2004.04.005
description: scientific article; zbMATH DE number 2091716