• Kenneth Ireland
  • Michael Rosen
Part of the Graduate Texts in Mathematics book series (GTM, volume 84)


Gauss first introduced the notion of congruence in Disquisitiones Arithmeticae (see Notes in Chapter 1). It is an extremely simple idea. Nevertheless, its importance and usefulness in number theory cannot be exaggerated.

This chapter is devoted to an exposition of the simplest properties of congruence. In Chapter 4, we shall go into the subject in more depth.


Chinese Remainder Theorem Congruence Class Principal Ideal Domain Congruence Modulo Arbitrary Commutative Ring 


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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Kenneth Ireland
  • Michael Rosen
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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