On the cycle structure of repeated exponentiation modulo a prime | Macquarie University ResearchOnline

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Title: On the cycle structure of repeated exponentiation modulo a prime
Related: Journal of number theory, Vol. 107, Issue 2 (2004), p.345-356
DOI: 10.1016/j.jnt.2004.04.005
Publisher: Academic Press
Date: 2004
FoR/RFCD Code(s): 010100 Pure Mathematics
Author/Creator: Chou, Wun-Seng
Author/Creator: Shparlinski, Igor E
Description: 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.
Description: 12 page(s)
Subject Keyword: 010100 Pure Mathematics
Subject Keyword: repeated powering
Subject Keyword: cycle structure
Subject Keyword: primes in arithmetic progressions
Resource Type: journal article
Organisation: Macquarie University. Dept. of Computing

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