Author(s): William W. Adams, Larry Joel Goldstein
Edition: 1st printing
Publisher: Prentice-Hall, Inc.
Year: 1976
Language: English
Commentary: same book as http://library.lol/main/DB8DB6E1EB3C7789266714E970F843BD but 1st printing and better scan
Pages: 380
City: Englewood Cliffs, New Jersey
Title
Contents
Preface
1. Introduction
1.1 What Is Number Theory?
1.2 Prerequisites
1.3 How to Use this Book
2. Divisibility and Primes
2.1 Introduction
2.2 Divisibility
2.3 The Greatest Common Divisor
2.4 Unique Factorization
Appendix A: Euler's Proof of the lnfinitude of Primes
3. Congruences
3.1 Introduction
3.2 Basic Properties of Congruences
3.3 Some Special Congruences
3.4 Solving Polynomial Congruences, I
3.5 Solving Polynomial Congruences, II
3.6 Primitive Roots
3.7 Congruences -- Some Historical Notes
4. The Law of Quadratic Reciprocity
4.1 Introduction
4.2 Basic Properties of Quadratic Residues
4.3 The Gauss Lemma
4.4 The Law of Quadratic Reciprocity
4.5 Applications to Diophantine Equations
5. Arithmetic Functions
5.1 Introduction
5.2 Multiplicative Arithmetic Functions
5.3 The Möbius Inversion Formula
5.4 Perfect and Amicable Numbers
6. A Few Diophantine Equafions
6.1 Introduction
6.2 The Equation x^2 + y^2 = z^2
6.3 The Equation x^4 + y^4 = z^2
6.4 The Equation x^2 + y^2 = n
6.5 The Equation x^2 + y^2 + z^2 + w^2 = n
6.6 Pell's Equation: x^2 - d y^2 = 1
Appendix B: Diophantine Approximations
Introduction to Chapters 7-11
7. The Gaussian Integers
7.1 Introduction
7.2 The Fundamental Theorem of Arithmetic in the Gaussian Integers
7.3. The Two-Square Problem Revisited
8. Arithmetic in Quadratic Fields
8.1 Introduction
8.2 Quadratic Fields
8.3 The Integers of a Quadratic Field
8.4 Binary Quadratic Forms
8.5 Modules
8.6 The Coefficient Ring of a Module
8.7 The Unit Theorem
8.8 Computing Elements of a Given Norm in a Module
9. Factorization Theory in Quadratic Fields
9.1 The Failure of Unique Factorization
9.2 Generalized Congruences and the Norm of a Module
9.3 Products and Sums of Modules
9.4 The Fundamental Factorization Theorem
9.5 The Prime Modules Belonging to O
9.6 Finiteness of the Class Number
10. Applications of the Factorization Theory to Diophantine Equations
10.1 The Diophantine Equation y^2 = x^3 + k
10.2 Proof of Fermat's Last Theorem for n = 3
10.3 Norm Form Equations
11. The Representation of Integers by Binary Quadratic Forms
11.1 Equivalence of Forms
11.2 Strict Similarity of Modules
11.3 The Correspondence Between Modules and Forms
11.4 The Representation of Integers by Binary Quadratic Forms
11.5 Composition Theory for Binary Quadratic Forms
Tables
Notation
Diophantine Equations
Index
