Integer Numbers: Congruences, Counting and Infinity
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.
KeywordsGreat Common Divisor Continuum Hypothesis Chinese Remainder Theorem White Ball Prime Number Theorem
Unable to display preview. Download preview PDF.