Cycles in Repeated Exponentiation Modulo pⁿ

2010/06/12 by Lev Glebsky, Glebsky, Lev
Mathematics · #11A05 #11A07 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A05 #msc:11A07

paper · pdf · doi:10.48550/arxiv.1006.2500

4 pages

arxiv created 2010/06/12 · arxiv updated 2010/06/15

Abstract

Given a number r, we consider the dynamical system generated by repeated exponentiations modulo r, that is, by the map u ↦ f_g(u), where f_g(u) ≡ g^u \pmod r and 0 ≤ f_g(u) ≤ r-1. The number of cycles of the defined above dynamical system is considered for r=pⁿ.

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