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Funktsional'nyi Analiz i ego Prilozheniya, 2003, Volume 37, Issue 1, Pages 1–18
DOI: https://doi.org/10.4213/faa132 (Mi faa132) 		 
This article is cited in 16 scientific papers (total in 17 papers)

Fermat–Euler Dynamical Systems and the Statistics of Arithmetics of Geometric Progressions

V. I. Arnol'd

Université Paris-Dauphine
Full-text PDF (215 kB) Citations (17)
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DOI: https://doi.org/10.4213/faa132
Abstract: Let $n$ be an integer. A Fermat–Euler dynamical system acts on the set of mod-$n$ residues coprime to $n$ by multiplication by a constant (which is also coprime to $n$). We study the dependence of the period and the number of orbits of this dynamical system on $n$. Theorems generalizing Fermat's little theorem, as well as empirical conjectures, are given.
Keywords: Euler function, Fermat's little theorem, chaotic behavior, weak asymptotics, quadratic residue, geometric progression, Young diagram.
Received: 23.10.2002
English version:
Functional Analysis and Its Applications, 2003, Volume 37, Issue 1, Pages 1–15
DOI: https://doi.org/10.1023/A:1022915825459
Bibliographic databases:
Document Type: Article
UDC: 511.3+517.938+519.21
Language: Russian
Citation: V. I. Arnol'd, “Fermat–Euler Dynamical Systems and the Statistics of Arithmetics of Geometric Progressions”, Funktsional. Anal. i Prilozhen., 37:1 (2003), 1–18; Funct. Anal. Appl., 37:1 (2003), 1–15
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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