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Elements of Number Theory

Publisher: 
Dover Publications
Number of Pages: 
240
Price: 
40.00
ISBN: 
0486495302

 

 

Date Received: 
Thursday, July 27, 2006
Reviewable: 
Yes
Include In BLL Rating: 
Yes
Ivan Matveevich Vinogradov
Publication Date: 
2003
Format: 
Hardcover
Audience: 
Category: 
Textbook
BLL Committee
03/23/2012
BLL Rating: 

 

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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Modify Date: 
Friday, March 23, 2012

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