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Chapter: Elementary Results About Prime Numbers
In this chapter, we will introduce prime numbers and prove that some basic results about them, in particular, the generalized Euclidean lemma, the fundamental theorem of arithmetic, and that there are infinitely many prime numbers.
Table of Contents
 Definition: Prime Numbers
 Theorem: Infinite Set of Prime Numbers
 Theorem: Fundamental Theorem of Arithmetic
 Definition: Canonical Representation of Natural Numbers, Factorization
 Definition: Subsets of Prime Numbers Not Dividing a Natural Number
 Definition: Canonical Representation of Positive Rational Numbers
 Definition: Floor and Ceiling Functions
 Proposition: Number of Multiples of a Given Number Less Than Another Number
 Proposition: Factorization of Greatest Common Divisor and Least Common Multiple
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References
Bibliography
 Scheid Harald: "Zahlentheorie", Spektrum Akademischer Verlag, 2003, 3rd Edition
 Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927