Redmond D. Number theory: an introduction

New York: M. Dekker, 1996. — 776 p.This reference text provides a detailed introduction to number theory--demonstrating how other areas of mathematics enter into the study of the properties of natural numbers.Historical Introduction
Primes and DivisibilityDivisibility
Prime numbers
Unique factorization
Some factorization methods, I
Additional problems
Congruences
Congruences
The Euler phi function
Congruences of the first degree
The Chinese remainder theorem
Polynomial congruences
Prime power moduli
Prime moduli
Primitive roots
Indices and binomial and exponential congruences
An application to cryptography
Pseudoprimes
Additional problems
Quadratic ResiduesQuadratic residues
The law of quadratic reciprocity
The Jacobi symbol
The Kronecker symbol
The solution of x^2 = D (mod m)
Additional problems
Approximation of Real NumbersFarey fractions
Approximation by rationals, I
Continued fractions
Periodic continued fractions
Approximation by rationals, II
Some factorization methods, II
Equivalent numbers
Decimal representation
Additional problems
Diophantine Equations, IPythagorean triangles
Related quadratic equations
The equation ax^2 + by^2 + cz^2 = 0
Additional problems
Diophantine Equations, IILinear equations
Sums of two squares
Sums of four squares
Sums of other numbers of squares
Binary quadratic forms
The equation x^2 - D y^2 = N
A Pythagorean triangle problem
The equation ax^2 + bxy + cy^2 + dx + ey + f = 0
Waring's problem
Additional problems
Arithmetic FunctionsDirichlet convolution
Multiplicative functions
Sum of divisors
Number of divisors
Euler's function
Characters
Trigonometrical sums
Additive functions
Linear recursion
Additional problems
The Average Order of Arithmetic FunctionsThe greatest integer function
Preliminaries
Sum of divisors function
The number of divisors functions
Euler's function
Lattice point problems
Additional problems
Prime Number TheoryBertrand's postulate and Chebychev's theorem
The prime number theorem
Primes in arithmetic progressions
Order of magnitude of multiplicative functions
Summatory functions of additive functions
Additional problems
An Introduction To Algebraic Number TheoryGeneral considerations
Quadratic number fields
Applications to Diophantine equations
Concluding remarks
Additional problems
Tables