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Description:

The theory of numbers is generally considered to be the 'purest' branch of pure mathematics and demands exactness of thought and exposition from its devotees. It is also one of the most highly active and engaging areas of mathematics. Now into it's eighth edition The Higher Arithmetic introduces the concepts and theorems of number theory in a way that does not require the reader to have an in-depth knowledge of the theory of numbers but also touches upon matters of deep mathematical significance. Since earlier editions, additional material written by J. H. Davenport has been added, on topics such as Wiles' proof of Fermat's Last Theorem, computers and number theory, and primality testing,… More Written to be accessible to the general reader, with only high school mathematics as prerequisite, this classic book is also ideal for undergraduate courses on number theory, and covers all the necessary material clearly and succinctly.Less

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Book details

Edition: 8th Copyright year: 2008 Publisher: Cambridge University Press Publication date: 10/23/2008 Binding: Paperback Pages: 250 Size: 6.00" wide x 8.75" long x 0.75" tall Weight: 0.748 Language: English

AuthorTable of Contents

Harold Davenport F.R.S. was the late Rouse Ball Professor of Mathematics at the University of Cambridge and Fellow of Trinity College.

Introduction

Factorization and the Primes

The laws of arithmetic

Proof by induction

Prime numbers

The fundamental theorem of arithmetic

Consequences of the fundamental theorem

Euclid's algorithm

Another proof of the fundamental theorem

A property of the H.C.F

Factorizing a number

The series of primes

Congruences

The congruence notation

Linear congruences

Fermat's theorem

Euler's function [phi] (m)

Wilson's theorem

Algebraic congruences

Congruences to a prime modulus

Congruences in several unknowns

Congruences covering all numbers

Quadratic Residues

Primitive roots

Indices

Quadratic residues

Gauss's lemma

The law of reciprocity

The distribution of the quadratic residues

Continued Fractions

Introduction

The general continued fraction

Euler's rule

The convergents to a continued fraction

The equation ax - by = 1

Infinite continued fractions

Diophantine approximation

Quadratic irrationals

Purely periodic continued fractions

Lagrange's theorem

Pell's equation

A geometrical interpretation of continued fractions

Sums of Squares

Numbers representable by two squares

Primes of the form 4k + 1

Constructions for x and y

Representation by four squares

Representation by three squares

Quadratic Forms

Introduction

Equivalent forms

The discriminant

The representation of a number by a form

Three examples

The reduction of positive definite forms

The reduced forms

The number of representations

The class-number

Some Diphantine Equations

Introduction

The equation x[superscript 2] + y[superscript 2] = z[superscript 2]

The equation ax[superscript 2] + by[superscript 2] = z[superscript 2]

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