My numbers, my friends我的数字,我的朋友
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作者： Paulo Ribenboim 著
出 版 社：
出版时间： 2000-6-9字数：版次：页数： 375印刷时间： 2000/06/09开本： 16开印次：纸张： 胶版纸I S B N ： 9780387989112包装： 平装内容简介
Paulo Ribenboim treats numbers as personal friends in thiscollection of expository essays. Topics include prime numbers,Fibonacci numbers (and the Arctic Ocean!), the classical workof Gauss on binary quadratic forms, Euler's famous primeproducing polynomial, powers, and irrational and tran-scendental numbers. The essays arewritten in a light languagewithout secrets and are thoroughly accessible to everyonewith an interest in numbers. Other books by the author are TheNew Book of Prime Number Records, The Little Book of BigPrimes, which have enjoyed a considerable success, and therecent Fermot's Lost Theorem for Amateurs (1999)
目录
Preface
1 The Fibonacci Numbers and the Aretic Ocean
1 Basic definitions
A Lucas sequences
B Speciallucas sequences
C Generalizations
2 Basic properties
A binet's formulas
B Degenerate Lucas sequences
C Growth and numerical calculations
D Algebraic relations.
E Divisibility properties
3 Prime divisors of Lucas sequences
A The sets P(U), P(V), and the rank ofappearance
B Primitive factors of Lucas sequences
4 Primes in Lucas sequences
5 Powers and powerful numbers in Lucas sequences
A General theorems for powers
B Explicit determination in special sequences
C Uniform explicit determination ofmultiples, squares, and square-classes forcertain families of Lucas sequences
D Powerful numbers in Lucas sequences
2 Representation of Real Numbers by Means ofFibonacci N-tubers
3 Prime Number Records
4 Selling Primes
5 Euler's Famous Prime Generating Polynomial
1 Quadratic extensions
2 Rings of integers
3 Discriminant
4 Decomposition of primes
A Properties of the norm
5 Units
6 The class number
A Calculation of the class n, lmber
B Determination of all quadratic fields withclass number 1
7 The main theorem
6 Gauss and the Class Number Problem
1 Introduction
2 Highlights of Gauss' life
3 Brief historical background
4 Binary quadratic forms
5 The fundamental problems
6 Equivalence of forms
7 Conditional solution of the fundamental problems
8 Proper equivalence classes of definite forms
A Another numerical example
9 Proper equivalence classes of indefinite forms
A Another numerical example
10 The automorph of a primitive form
11 Composition of proper equivalence classes ofprimitive forms