Primitive Roots

  • Tom M. Apostol
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Let a and m be relatively prime integers, with m ≥ 1, and consider all the positive powers of a:
$$a,{a^2}.{a^3},...$$
We know, from the Euler — Fermat theorem, that aϕ(m) ≡ 1 (mod m). However, there may be an earlier power a f such that a f ≡ 1 (mod m). We are interested in the smallest positive f with this property.

Keywords

Primitive Root Quadratic Residue Dirichlet Character Primitive Character Linear Congruence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1976

Authors and Affiliations

  • Tom M. Apostol
    • 1
  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

Personalised recommendations