Elements of number theory

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Cover Title page Preface Chapter I DIVISIBILITY THEORY l. Basic Concepts and Theorems 2. The Greatest Common Divisor 3. The Least Common Multiple 4. The Relation of Euc!id's Aigorithm 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 l. 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 l. 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 l. 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 l. General Theorems 2. Primitive Roots Modulo p^a and 2p^a 3. Evaluation of Primitive Roots for the Moduli p^a and 2p^a 4. Indices for the Moduli p^a and 2p^a 1l0 5. Consequences of the Preceding Theory 6. Indices Modulo 2^a 1l6 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