Book:Ivan Niven/An Introduction to the Theory of Numbers/Third Edition
Jump to navigation
Jump to search
Ivan Niven and Herbert S. Zuckerman: An Introduction to the Theory of Numbers (3rd Edition)
Published $\text {1972}$
Subject Matter
Contents
- 1. Divisibility
- 1.1 Introduction
- 1.2 Divisibility
- 1.3 Primes
- 2. Congruences
- 2.1 Congruences
- 2.2 Solutions of Congruences
- 2.3 Congruences of Degree I
- 2.4 The Function $\phi(n)$
- 2.5 Congruences of Higher Degree
- 2.6 Prime Power Moduli
- 2.7 Prime Modulus
- 2.8 Congruences of Degree Two, Prime Modulus
- 2.9 Power Residues
- 2.10 Number Theory from an Algebraic Viewpoint
- 2.11 Multiplicative Groups, Rings, and Fields
- 3. Quadratic Reciprocity
- 3.1 Quadratic Residues
- 3.2 Quadratic Reciprocity
- 3.3 The Jacobi Symbol
- 4. Some Functions of Number Theory
- 4.1 Greatest Integer Function
- 4.2 Arithmetic Functions
- 4.3 The Moebius Inversion Formula
- 4.4 The Multiplication of Arithmetic Functions
- 4.5 Recurrence Functions
- 5. Some Diophantine Equations
- 5.1 Diophantine Equations
- 5.2 The Equation $ax + by = c$
- 5.3 Positive Solutions
- 5.4 Other Linear Equations
- 5.5 The Equation $x^2 + y^2 = z^2$
- 5.6 The Equation $x^4 + y^4 = z^2$
- 5.7 Sums of Four and Five Squares
- 5.8 Waring's Problem
- 5.9 Sum of Fourth Powers
- 5.10 Sum of Two Squares
- 5.11 The Equation $4x^2 + y^2 = n$
- 5.12 The Equation $ax^2 + by^2 + cz^2 = 0$
- 5.13 Binary Quadratic Forms
- 5.14 Equivalence of Quadratic Forms
- 6. Farey Fractions and Irrational Numbers
- 6.1 Farey Sequences
- 6.2 Rational Approximations
- 6.3 Irrational Numbers
- 6.4 Coverings of the Real Line
- 7. Simple Continued Fractions
- 7.1 The Euclidean Algorithm
- 7.2 Uniqueness
- 7.3 Infinite Continued Fractions
- 7.4 Irrational Numbers
- 7.5 Approximations to Irrational Numbers
- 7.6 Best Possible Approximations
- 7.7 Periodic Continued Fractions
- 7.8 Pell's Equation
- 7.9 Numerical Computation
- 8. Elementary Remarks on the Distribution of Primes
- 8.1 The Function $\pi(x)$
- 8.2 The Sequence of Primes
- 8.3 Bertrand's Postulate
- 9. Algebraic Numbers
- 9.1 Polynomials
- 9.2 Algebraic Numbers
- 9.3 Algebraic Number Fields
- 9.4 Algebraic Integers
- 9.5 Quadratic Fields
- 9.6 Units in Quadratic Fields
- 9.7 Primes in Quadratic Fields
- 9.8 Unique Factorization
- 9.9 Primes in Quadratic Fields Having the Unique Factorization Property
- 9.10 The Equation $x^3 + y^3 = z^3$
- 10. The Partition Function
- 10.1 Partitions
- 10.2 Graphs
- 10.3 Formal Power Series and Euler's Identity
- 10.4 Euler's Formula
- 10.5 Jacobi's Formula
- 10.6 A Divisibility Property
- 11. The Density of Sequences of Integers
- 11.1 Asymptotic Density
- 11.2 Square-Free Integers
- 11.3 Sets of Density Zero
- 11.4 Schnirelmann Density and the $\alpha\beta$ Theorem
- Miscellaneous Problems
- Special Topics
- General References
- Answers to Problems
- Index
Further Editions
- 1960: Ivan Niven and Herbert S. Zuckerman: An Introduction to the Theory of Numbers
- 1966: Ivan Niven and Herbert S. Zuckerman: An Introduction to the Theory of Numbers (2nd ed.)
- 1980: Ivan Niven and Herbert S. Zuckerman: An Introduction to the Theory of Numbers (4th ed.)
- 1991: Ivan Niven, Herbert S. Zuckerman and Hugh L. Montgomery: An Introduction to the Theory of Numbers (5th ed.)