A friendly introduction to number theory

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A friendly introduction to number theory / Joseph H. Silverman

版:: 2nd ed
資料種別:: 図書
出版情報:: Upper Saddle River, NJ : Prentice Hall, c2001
形態:: vii, 386 p. ; 24 cm
著者名:: Silverman, Joseph H., 1955- <DA00119648>
ISBN:: 9780130309549 [0130309540]
書誌ID:: BA52503074

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注記:

Includes bibliographical references and index

主題:

Number theory

言語:

英語

目次情報:

Preface

Introduction

What Is Number Theory? / Chapter 1.：

Pythagorean Triples / Chapter 2.：

Pythagorean Triples and the Unit Circle / Chapter 3.：

Sums of Higher Powers and Fermat's Last Theorem / Chapter 4.：

Divisibility and the Greatest Common Divisor / Chapter 5.：

Linear Equations and the Greatest Common Divisor / Chapter 6.：

Factorization and the Fundamental Theorem of Arithmetic / Chapter 7.：

Congruences / Chapter 8.：

Congruences, Powers, and Fermat's Little Theorem / Chapter 9.：

Congruences, Powers, and Euler's Formula / Chapter 10.：

Euler's Phi Function / Chapter 11.：

Prime Numbers / Chapter 12.：

Counting Primes / Chapter 13.：

Mersenne Primes / Chapter 14.：

Mersenne Primes and Perfect Numbers / Chapter 15.：

Powers Modulo m and Successive Squaring / Chapter 16.：

Computing k[superscript th] Roots Modulo m / Chapter 17.：

Powers, Roots, and "Unbreakable" Codes / Chapter 18.：

Euler's Phi Function and Sums of Divisors / Chapter 19.：

Powers Modulo p and Primitive Roots / Chapter 20.：

Primitive Roots and Indices / Chapter 21.：

Squares Modulo p / Chapter 22.：

Is - 1 a Square Modulo p? Is 2? / Chapter 23.：

Quadratic Reciprocity / Chapter 24.：

Which Primes Are Sums of Two Squares? / Chapter 25.：

Which Numbers Are Sums of Two Squares? / Chapter 26.：

The Equation X[superscript 4] + Y[superscript 4] = Z[superscript 4] / Chapter 27.：

Square-Triangular Numbers Revisited / Chapter 28.：

Pell's Equation / Chapter 29.：

Diophantine Approximation / Chapter 30.：

Diophantine Approximation and Pell's Equation / Chapter 31.：

Primality Testing and Carmichael Numbers / Chapter 32.：

Number Theory and Imaginary Numbers / Chapter 33.：

The Gaussian Integers and Unique Factorization / Chapter 34.：

Irrational Numbers and Transcendental Numbers / Chapter 35.：

Binomial Coefficients and Pascal's Triangle / Chapter 36.：

Fibonacci's Rabbits and Linear Recurrence Sequences / Chapter 37.：

Generating Functions / Chapter 38.：

Sums of Powers / Chapter 39.：

Cubic Curves and Elliptic Curves / Chapter 40.：

Elliptic Curves with Few Rational Points / Chapter 41.：

Points on Elliptic Curves Modulo p / Chapter 42.：

Torsion Collections Modulo p and Bad Primes / Chapter 43.：

Defect Bounds and Modularity Patterns / Chapter 44.：

Elliptic Curves and Fermat's Last Theorem / Chapter 45.：

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