Book:Ivan Niven/An Introduction to the Theory of Numbers/Fifth Edition
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Ivan Niven, Herbert S. Zuckerman and Hugh L. Montgomery: An Introduction to the Theory of Numbers (5th Edition)
Published $\text {1991}$, Wiley
- ISBN 978-0471625469
Subject Matter
Contents
- Notation
- 1 Divisibility
- 1.1 Introduction
- 1.2 Divisibility
- 1.3 Primes
- 1.4 The Binomial Theorem
- Notes on Chapter 1
- 2 Congruences
- 2.1 Congruences
- 2.2 Solutions of Congruences
- 2.3 The Chinese Remainder Theorem
- 2.4 Techniques of Numerical Calculation
- 2.5 Public-Key Cryptography
- 2.6 Prime Power Moduli
- 2.7 Prime Modulus
- 2.8 Primitive Roots and Power Residues
- 2.9 Congruences of Degree Two, Prime Modulus
- 2.10 Number Theory from an Algebraic Viewpoint
- 2.11 Groups, Rings, and Fields
- Notes on Chapter 2
- 3 Quadratic Reciprocity and Quadratic Forms
- 3.1 Quadratic Residues
- 3.2 Quadratic Reciprocity
- 3.3 The Jacobi Symbol
- 3.4 Binary Quadratic Forms
- 3.5 Equivalence and Reduction of Binary Quadratic Forms
- 3.6 Sums of Two Squares
- 3.7 Positive Definite Binary Quadratic Forms
- Notes on Chapter 3
- 4 Some Functions of Number Theory
- 4.1 Greatest Integer Function
- 4.2 Artihmetic Functions
- 4.3 The Möbius Inversion Formula
- 4.4 Recurrence Functions
- 4.5 Combinatorial Number Theory
- Notes on Chapter 4
- 5 Some Diophantine Equations
- 5.1 The Equation $ax + by = c$
- 5.2 Simultaneous Linear Equations
- 5.3 Pythagorean Triangles
- 5.4 Assorted Examples
- 5.5 Ternary Quadratic Forms
- 5.6 Rational Points on Curves
- 5.7 Elliptic Curves
- 5.8 Factorization Using Elliptic Curves
- 5.9 Curves of Genus Greater Than $1$
- Notes on Chapter 5
- 6 Farey Fractions and Irrational Numbers
- 6.1 Farey Sequences
- 6.2 Rational Approximations
- 6.3 Irrational Numbers
- 6.4 The Geometry of Numbers
- Notes on Chapter 6
- 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
- Notes on Chapter 7
- 8 Primes and Multiplicative Number Theory
- 8.1 Elementary Prime Number Estimates
- 8.2 Dirichlet Series
- 8.3 Estimates of Arithmetic Functions
- 8.4 Primes in Arithmetic Progressions
- Notes on Chapter 8
- 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 $x^3 + y^3 = z^3$
- Notes on Chapter 9
- 10 The Partition Function
- 10.1 Parittions
- 10.2 Ferrers Graphs
- 10.3 Formal Power Series, Generating Functions, and Euler's Identity
- 10.4 Euler's Formula; Bounds on $p(n)$
- 10.5 Jacobi's Formula
- 10.6 A Divisibiity Property
- Notoes on Chapter 10
- 11 The Density of Sequences of Integers
- 11.1 Asymptotic Density
- 11.2 Schnirelmann Density and the $\alpha\beta$ Theorem
- Notes on Chapter 11
- Appendices
- A.1 The Fundamental Theorem of Algebra
- A.2 Symmetric Functions
- A.3 A Special Value of the Riemann Zeta Function
- A.4 Linear Recurrences
- General References
- Hints
- Answers
- 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.)
- 1972: Ivan Niven and Herbert S. Zuckerman: An Introduction to the Theory of Numbers (3rd ed.)
- 1980: Ivan Niven and Herbert S. Zuckerman: An Introduction to the Theory of Numbers (4th ed.)