1: Chapters Last updated Aug 17, 2021 Save as PDF Preface 1.1: Basic Axioms for Z Page ID82838 ( \newcommand{\kernel}{\mathrm{null}\,}\) 1.1: Basic Axioms for Z1.2: Proof by Induction1.3: Elementary Divisibility Properties1.4: The Floor and Ceiling of a Real Number1.5: The Division Algorithm1.6: Greatest Common Divisor1.7: The Euclidean Algorithm1.8: Bezout's Lemma1.9: Blankinship's Method1.10: Prime Numbers1.11: Unique Factorization1.12: Fermat Primes and Mersenne Primes1.13: The Functions σ and τ1.14: Perfect Numbers and Mersenne Primes1.15: Congruences1.16: Divisibility Tests for 2, 3, 5, 9, 111.17: Divisibility Tests for 7 and 131.18: More Properties of Congruences1.19: Residue Classes1.20: Zm and Complete Residue Systems1.21: Addition and Multiplication in Zm1.22: The Groups Um1.23: Two Theorems of Euler and Fermat1.24: Probabilistic Primality Tests1.25: The Base b Representation of n1.26: Computation of aN mod m1.27: The RSA Scheme1.28: A Rings and Groups