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

Subject Matter

 * Number Theory

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