Integer Numbers: Congruences, Counting and Infinity

  • Mariano Giaquinta
  • Giuseppe Modica


In this chapter we collect a few complements to the theory of integers. In Section 3.1, after discussing Euclid’s algorithm,and the fundamental theorem of arithmetic,we deal with Euler’s function and some of its applications to public key cryptography. In Section 3.2 we introduce a few basic elements of combinatorics, that is, the calculus of arrangements of a finite number of objects. Finally, in Section 3.3, we illustrate the notion of cardinality (or number of elements) of a (not necessarily finite) set introducing some of the concepts involved in Cantor’s theory of infinity.


Great Common Divisor Continuum Hypothesis Chinese Remainder Theorem White Ball Prime Number Theorem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Mariano Giaquinta
    • 1
  • Giuseppe Modica
    • 2
  1. 1.Dipartimento di MatematicaScuola Normale SuperiorePisaItaly
  2. 2.Dipartimento di Matematica ApplicataUniversità degli Studi di FirenzeFirenzeItaly

Personalised recommendations