On the cycle structure of repeated exponentiation modulo a prime

Wun Seng Chou, Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)345-356
Number of pages12
JournalJournal of Number Theory
Issue number2
Publication statusPublished - Aug 2004


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