Book:Ivan Niven/An Introduction to the Theory of Numbers/Fifth Edition

Subject Matter

 * Number Theory

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