Higher Arithmetic An Introduction to the Theory of Numbers

ISBN-10: 0521722365

ISBN-13: 9780521722360

Edition: 8th 2008 (Revised)

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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, 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.

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Book details

List price: $71.99
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: 0.792
Language: English

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]
Elliptic equations and curves
Elliptic equations modulo primes
Fermat's Last Theorem
The equation x[superscript 3] + y[superscript 3] = z[superscript 3] + w[superscript 3]
Further developments
Computers and Number Theory
Introduction
Testing for primality
'Random' number generators
Pollard's factoring methods
Factoring and primality via elliptic curves
Factoring large numbers
The Diffie-Hellman cryptographic method
The RSA cryptographic method
Primality testing revisited
Exercises
Hints
Answers
Bibliography
Index
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