Integer Numbers: Congruences, Counting and Infinity

Mariano Giaquinta and Giuseppe Modica
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Mariano Giaquinta: Scuola Normale Superiore, Dipartimento di Matematica
Giuseppe Modica: Università degli Studi di Firenze, Dipartimento di Matematica Applicata

Chapter 3 in Mathematical Analysis, 2004, pp 71-120 from Springer

Abstract: 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.

Keywords: Great Common Divisor; Continuum Hypothesis; Chinese Remainder Theorem; White Ball; Prime Number Theorem (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-4414-7_3

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DOI: 10.1007/978-0-8176-4414-7_3

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