Treffer: fermat euler dynamical systems and the statistics of arithmetics of geometric progressions: Fermat-Euler dynamical systems and the statistics of arithmetics of geometric progressions

Title:
fermat euler dynamical systems and the statistics of arithmetics of geometric progressions: Fermat-Euler dynamical systems and the statistics of arithmetics of geometric progressions
Authors:
Vladimir I. Arnold
Source:
Functional Analysis and Its Applications. 37(1):1-15
Publisher Information:
Springer US, New York, NY, 2003.
Publication Year:
2003
Subject Terms:
Euler function, geometric progression, weak asymptotics, Relations of ergodic theory with number theory and harmonic analysis, Fermat's little theorem, chaotic behavior, Young diagram, Elementary number theory, quadratic residue
Document Type:
Fachzeitschrift Article
File Description:
application/xml
ISSN:
0016-2663
DOI:
10.1023/a:1022915825459
Access URL:
https://link.springer.com/article/10.1023/A:1022915825459
Accession Number:
edsair.dedup.wf.002..f3070cefcca03edaa8f3d1ce19498319
Database:
OpenAIRE

Weitere Informationen

The integer \(n\) is said to belong to the set \((N+)\) if \(N\) is the largest integer such that \(a^{\varphi(n)/N}\equiv+1\pmod n\), where \(a\) is prime to \(n\). Similarly the set \((M-)\) is that for which \(M\) is the largest integer such that \(a^{\varphi(n)/M}\equiv -1\pmod n\). In what follows only \(a=2\) is considered. Various properties of the sets \((N+)\) and \((M-)\) are proved and some problems are posed.