Elementary number theory

Index......Page 
Front Matter......Page 0001.tif.djvu
Publisher\'s Preface......Page 0003.tif.djvu
Preface......Page 0004.tif.djvu
Contents......Page 0007.tif.djvu
Part One - Foundations of Number Theory......Page 0009.tif.djvu
I. The Greatest Common Divisor of Two Numbers......Page 0010.tif.djvu
II. Prime Numbers and Factorization into Prime Factors......Page 0017.tif.djvu
III. The Greatest Common Divisor of Several Numbers......Page 0025.tif.djvu
IV. Number-Theoretic Functions......Page 0028.tif.djvu
V. Congruences......Page 0036.tif.djvu
VI. Quadratic Residues......Page 0052.tif.djvu
VII. Pell\'s Equation......Page 0075.tif.djvu
Part Two - Brun\'s Theorem and Dirichlet\'s Theorem......Page 0084.tif.djvu
Introduction......Page 0085.tif.djvu
I. Some Elementary Inequalities of Prime-Number Theory......Page 0086.tif.djvu
II. Brun\'s Theorem on Prime Pairs......Page 0092.tif.djvu
III. Dirichlet\'s Theorem on the Prime Numbers of an Arithmetic Progression......Page 0102.tif.djvu
§1. Further Theorems on Congruences......Page 102
§2. Characters......Page 0107.tif.djvu
§3. L-Series......Page 0113.tif.djvu
§4. Dirichlet\'s Proof......Page 0123.tif.djvu
Part Three - Decomposition into Two, Three, and Four Squares......Page 0124.tif.djvu
Introduction......Page 0125.tif.djvu
I. Farey Fractions......Page 0127.tif.djvu
II. Decomposition into Two Squares......Page 0131.tif.djvu
III. Decomposition into Four Squares......Page 0137.tif.djvu
Introduction......Page 137
§1. Lagrange\'s Theorem......Page 0138.tif.djvu
§2. Determination of the Number of Solutions......Page 0142.tif.djvu
IV. Decomposition into Three Squares......Page 0147.tif.djvu
§1. Equivalence of Quadratic Forms......Page 147
§2. A Necessary Condition for Decomposability into Three Squares......Page 0157.tif.djvu
§3. The Necessary Condition is Sufficient......Page 0158.tif.djvu
Part Four - Class Number of Binary Quadratic Forms......Page 0161.tif.djvu
Introduction......Page 0162.tif.djvu
I. Factorable and Unfactorable Forms......Page 0165.tif.djvu
II. Classes of Forms......Page 0167.tif.djvu
III. The Finiteness of the Class Number......Page 0170.tif.djvu
IV. Primary Representations by Forms......Page 0175.tif.djvu
V. Representations of h(d) in terms of K(d)......Page 0186.tif.djvu
VI. Gaussian Sums......Page 0192.tif.djvu
Appendix......Page 0197.tif.djvu
Introduction......Page 197
§1. Kronecker\'s Proof......Page 0198.tif.djvu
§2. Schur\'s Proof......Page 0202.tif.djvu
§3. Merten\'s Proof......Page 0208.tif.djvu
VII. Reduction to Fundamental Discriminants......Page 0214.tif.djvu
VIII. The Determination of K(d) for Fundamental Discriminants......Page 0216.tif.djvu
IX. Final Formulas for the Class Number......Page 0222.tif.djvu
Appendix - Exercises......Page 0225.tif.djvu
Exercises for Part One......Page 0226.tif.djvu
Exercises for Chapter I......Page 226
Exercises for Chapter II......Page 0227.tif.djvu
Exercises for Chapter IV......Page 0228.tif.djvu
Exercises for Chapter V......Page 0229.tif.djvu
Exercises for Chapter VI......Page 0231.tif.djvu
Exercises for Chapter VII......Page 0233.tif.djvu
Exercises for Part Two......Page 0235.tif.djvu
Exercises for Chapter II......Page 0236.tif.djvu
Exercises for Chapter III......Page 0237.tif.djvu
Exercises for Part Three......Page 0240.tif.djvu
Exercises for Chapter III......Page 0241.tif.djvu
Exercises for Chapter IV......Page 0242.tif.djvu
Index......Page 0244.tif.djvu
Index of Conventions......Page 0245.tif.djvu
Index of Symbols......Page 0246.tif.djvu