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Other titles in the Dover Phoenix Editions series:
Elements of Number Theory (Dover Phoenix Editions)
Synopses & ReviewsPublisher Comments:"A very welcome addition to books on number theory."--Bulletin, American Mathematical Society Clear and detailed in its exposition, this text can be understood by readers with no background in advanced mathematics; only a small part requires a working knowledge of calculus. One of the most valuable characteristics of this book is its stress on learning number theory by means of demonstrations and problems. More than 200 problems and full solutions appear in the text, plus 100 numerical exercises. Some of these exercises deal with estimation of trigonometric sums and are especially valuable as introductions to more advanced studies. Translation of 1949 Russian edition. Synopsis:Clear, detailed exposition that can be understood by readers with no background in advanced mathematics. More than 200 problems and full solutions, plus 100 numerical exercises. 1949 edition. Synopsis:Clear and detailed in its exposition, this text requires no background in advanced mathematics. It features more than 200 problems and full solutions, plus 100 numerical exercises. Some of these exercises deal with estimation of trigonometric sums and are especially valuable as introductions to more advanced studies. 1949 edition. Synopsis:Clear, detailed exposition that can be understood by readers with no background in advanced mathematics. More than 200 problems and full solutions, plus 100 numerical exercises. "A very welcome addition to books on number theory."--Bulletin, American Mathematical Society Contents: 1. Divisibility Theory. 2. Important Number-Theoretical Functions. 3. Congruences. 4. Congruences in One Unknown. 5. Congruences of Second Degree. 5. Primitive Roots and Indices. Solutions of the Problems. Answers to the Numerical Exercises. Tables of Indices. Tables of Primes
Table of ContentsPreface 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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