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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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Add Elements of number theory, 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, Elements of number theory to the inventory that you are selling on WonderClubX
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Add Elements of number theory, 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, Elements of number theory to your collection on WonderClub |