Affordable Access

Publisher Website

On the cycle structure of repeated exponentiation modulo a prime

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
107
Issue
2
Identifiers
DOI: 10.1016/j.jnt.2004.04.005
Keywords
  • Repeated Powering
  • Cycle Structure
  • Primes In Arithmetic Progressions
Disciplines
  • Mathematics

Abstract

Abstract In a recent work, Shallit and Vasiga have obtained several results about tails and cycles in orbits of repeated squaring. Some of these results have been based on the Extended Riemann Hypothesis. Here, we extend their result to repeated exponentiation with any fixed exponent e and also show that in fact classical unconditional results about the distribution of primes in arithmetic progressions, combined with very elementary arguments, are quite sufficient to generalise and give an unconditional proof of their asymptotic formulas.

There are no comments yet on this publication. Be the first to share your thoughts.