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Integer Numbers: Congruences, Counting and Infinity

In: Mathematical Analysis

Author

Listed:
  • Mariano Giaquinta

    (Scuola Normale Superiore, Dipartimento di Matematica)

  • Giuseppe Modica

    (Università degli Studi di Firenze, Dipartimento di Matematica Applicata)

Abstract

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.

Suggested Citation

  • Mariano Giaquinta & Giuseppe Modica, 2004. "Integer Numbers: Congruences, Counting and Infinity," Springer Books, in: Mathematical Analysis, chapter 3, pages 71-120, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4414-7_3
    DOI: 10.1007/978-0-8176-4414-7_3
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