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Complex Euler’s groups and values of Euler’s function at complex integer Gauss points

  • Vladimir I. Arnold
Article
  • 70 Downloads

Abstract

The complex Euler group is defined associating to an integer complex number z the multiplicative group of the complex integers residues modulo z, relatively prime to z. This group is calculated for z=(3+0i) n : it is isomorphic to the product of three cyclic group or orders (8, 3 n−1 and 3 n−1).

Keywords

Gauss integers Euler function Complex prime numbers Fermat/Euler theorem Geometry of formulae Squaring graphs 

Mathematics Subject Classification (2000)

11A05 11A25 11A41 11R04 

Copyright information

© PHASIS Verlag UG 2011

Authors and Affiliations

  • Vladimir I. Arnold
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

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