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Publisher:

Dover Publications

Publication Date:

2003

Number of Pages:

240

Format:

Hardcover

Price:

40.00

ISBN:

0486495302

Category:

Textbook

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by , on ]

BLL Committee

03/23/2012

Preface | ||||||||

Chapter I | ||||||||

DIVISIBILITY THEORY | ||||||||

§ 1. | Basic Concepts and Theorems | |||||||

§ 2. | The Greatest Common Divisor | |||||||

§ 3. | The Least Common Multiple | |||||||

§ 4. | The Relation of Euclid's Algorithm to Continued Fractions | |||||||

§ 5. | Prime Numbers | |||||||

§ 6. | The Unicity of Prime Decomposition | |||||||

Problems for Chapter I | ||||||||

Numerical Exercises for Chapter I | ||||||||

Chapter II | ||||||||

IMPORTANT NUMBER-THEORETICAL FUNCTIONS | ||||||||

§ 1. | "The Functions x ,x" | |||||||

§ 2. | Sums Extended over the Divisors of a Number | |||||||

§ 3. | The Möbius Function | |||||||

§ 4. | The Euler Function | |||||||

Problems for Chapter II | ||||||||

Numerical Exercises for Chapter II | ||||||||

Chapter III | ||||||||

CONGRUENCES | ||||||||

§ 1. | Basic Concepts | |||||||

§ 2. | Properties of Congruences Similar to those of Equations | |||||||

§ 3. | Further Properties of Congruences | |||||||

§ 4. | Complete Systems of Residues | |||||||

§ 5. | Reduced Systems of Residues | |||||||

§ 6. | The Theorems of Euler and Fermat | |||||||

Problems for Chapter III | ||||||||

Numerical Exercises for Chapter III | ||||||||

Chapter IV | ||||||||

CONGRUENCES IN ONE UNKNOWN | ||||||||

§ 1. | Basic Concepts | |||||||

§ 2. | Congruences of the First Degree | |||||||

§ 3. | Systems of Congruences of the First Degree | |||||||

§ 4. | Congruences of Arbitrary Degree with Prime Modulus | |||||||

§ 5. | Congruences of Arbitrary Degree with Composite Modulus | |||||||

Problems for Chapter IV | ||||||||

Numerical Exercises for Chapter IV | ||||||||

Chapter V | ||||||||

CONGRUENCES OF SECOND DEGREE | ||||||||

§ 1. | General Theorems | |||||||

§ 2. | The Legendre Symbol | |||||||

§ 3. | The Jacobi Symbol | |||||||

§ 4. | The Case of Composite Moduli | |||||||

Problems for Chapter V | ||||||||

Numerical Exercises for Chapter V | ||||||||

Chapter VI | ||||||||

PRIMITIVE ROOTS AND INDICES | ||||||||

§ 1. | General Theorems | |||||||

§ 2. | Primitive Roots Modulo pa and 2pa | |||||||

§ 3. | Evaluation of Primitive Roots for the Moduli pa and 2pa | |||||||

§ 4. | Indices for the Moduli pa and 2pa | |||||||

§ 5. | Consequences of the Preceding Theory | |||||||

§ 6. | Indices Modulo 2a | |||||||

§ 7. | Indices for Arbitrary Composite Modulus | |||||||

Problems for Chapter VI | ||||||||

Numerical Exercises for Chapter VI | ||||||||

SOLUTIONS OF THE PROBLEMS | ||||||||

Solutions for Chapter I | ||||||||

Solutions for Chapter II | ||||||||

Solutions for Chapter III | ||||||||

Solutions for Chapter IV | ||||||||

Solutions for Chapter V | ||||||||

Solutions for Chapter VI | ||||||||

ANSWERS TO THE NUMERICAL EXERCISES | ||||||||

Answers for Chapter I | ||||||||

Answers for Chapter II | ||||||||

Answers for Chapter III | ||||||||

Answers for Chapter IV | ||||||||

Answers for Chapter V | ||||||||

Answers for Chapter VI | ||||||||

TABLES OF INDICES | ||||||||

TABLES OF PRIMES <4000 AND THEIR LEAST PRIMITIVE ROOTS | ||||||||

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