高等算術（第8版）

《高等算術（第8版）》是2016年世界圖書出版公司出版的著作，作者是[英] Davenport，H.。

基本介紹

• 書名：《高等算術（第8版）》
• 作者：[英]Davenport，H.
• 出版社：世界圖書出版公司
• 出版時間：2016年07月01日
• ISBN：9787519205317 

內容簡介

《高等算術（第8版 英文版）》介紹了一些的數論問題，適合不同層次的讀者閱讀。一方面，作者不需要寬泛的數學知識；事實上，只要在數學方面接受過正規的學校教育就足夠了。另一方面，作者探討了一些真正的數學興趣問題，並以易讀懂的方式講解，因此，數學知識豐富的作者在閱讀此書時會感到非常愉悅和有益。《高等算術（第8版 英文版）》中幾個值得注意的點：數學歸納法的詳細講述和通過該法證明的獨特的因子分解定理。

目錄

Introduction

Ⅰ Factorization and the Primes

1．The laws of arithmetic

2．Proof by induction

3．Prime numbers

4．The fundamental theorem of arithmetic

5．Consequences of the fundamental theorem

6．Euclid's algorithm

7．Another proof of the fundamental theorem

8．A property of the H．C．F

9．Factorizing a number

10．The series of primes

Ⅱ Congruences

1．The congruence notation

2．Linear congruences

3．Fermat's theorem

4．Euler's function φ（m）

5．Wilson's theorem

6．Algebraic congruences

7．Congruences to a prime modulus

8．Congruences in several unknowns

9．Congruences covering all numbers

Ⅲ Quadratic Residues

1．Primitive roots

2．Indices

3．Quadratic residues

4．Gauss's lemma

5．The law of reciprocity

6．The distribution of the quadratic residues

Ⅳ Continued Fractions

1．Introduction

2．The general continued fraction

3．Euler's rule

4．The convergents to a continued traction

5．The equation ax-by=1

6．Infinite continued fractions

7．Diophantine approximation

8．Quadratic irrationals

9．Purely periodic continued fractions

10．Lagrange's theorem

11．Pell's equation

12．A geometricalinterpretation of continued fractions

Ⅴ Sums of Squares

1．Numbers representable by two squares

2．Primes of the form 4k+1

3．Constructions for x and y

4．Representation by four squares

5．Representation by three squares

Ⅵ Quadratic Forms

1．Introduction

2．Equivalent forms

3．The discriminant

4．The representation of a number by a form

5．Three examples

6．The reduction of positive definite forms

7．The reduced forms

8．The number of representations

9．The class-number

Ⅶ Some Diophantine Equations

1．Introduction

2．The equation x2+y2=z2

3．The equation ax2+by2=z2

4．Elliptic equations and curves

5．Elliptic equations modulo primes

6．Fermat's Last Theorem

7．The equation x3+y3=z3+w3

8．Further developments

Ⅷ Computers and Number Theory

1．Introduction

2．Testing for primality

3．‘Random’ number generators

4．Pollard's factoring methods

5．Factoring and primality via elliptic curves

6．Factoring large numbers

7．The Diffie-Hellman cryptographic method

8．The RSA cryptographic method

9．Primality testing revisited

Exercises

Hints

Answers

Bibliography

Index