Original edition, entitled A FRIENDLY INTRODUCTION TO NUMBER THEORY, 4E, 9780321816191 by SILVERMAN, JOSEPH H., published by Pearson Education, Inc, publishing as Pearson, Copyright 2013. All rights reserved. No part of this book may be reproduced o
目录
Preface Flowchart ofChapter Dependencies Introduction 1 What Is Number Theory? 2 Pythagorean Triples 3 Pythagorean Triples and the Unit Circle 4 Sums ofHigher Powers and Fermat’S Last Theorem 5 Divisibility and the Greatest Common Divisor 6 Linear Equations and the Greatest Common Divisor 7 Factorization and the Fundamental Theorem ofArithmetic 8 Congruences 9 Congruences，Powers，andFermat’S LittleTheorem 10 Congruences，Powers，and Euler’S Formula 11 Euler’S Phi Function and the Chinese Remainder Theorem 12 Prime Numbers 13 Counting Primes 14 Mersenne Primes 15 Mersenne Primes and Perfect Numbers 16 Powers Modulo m and Successive Squaring 17 Computing kth Roots Modulo m 18 Powers，Roots，and“Unbreakable Codes l9 Primality Testing and Carmichael Numbers 20 Squares Modulo р 21 Is-l a Square Modulo р?Is 2? 22 Quadratic Reciprocity 23 Proofof Quadratic Reciprocity 24 Which Primes Are Sums ofTwo Squares7 25 Which Numbers Are Sums ofTwo Squares7 26 As Easy as One，TwO，Three 27 Euler’S Phi Function and Sums of Divisors 28 Powers Modulo р and Primitive Roots 29 Primitive Roots and Indices 30 The Equation X4+Y4=Z4 3l Square-Triangular Numbers Revisited 32 Pell’S Equation 33 Diophantine Approximation 34 Diophantine Approximation and Pell’S Equation 35 Number Theory and Imaginary Numbers 36 The Gaussian Integers and Unique Factorization 37 Irrational Numbers and Transcendental Numbers 38 Binomial Coefficients and Pascal’S Triangle 39 Fibonacci’S Rabbits and Linear Recurrence Sequences 40 Oh，What a Beautiful Function 41 Cubic Curves and Elliptic Curves 42 Elliptic Curves with Few Rational Points 43 Points on Elliptic Curves Modulo р 44 Torsion Collections Modulo р and Bad Primes 45 Defect Bounds and Modularity Patterns 46 Elliptic Curves and Fermat’S Last Theorem Further Reading Index 47 The Topsy-Turvy World of Continued Fractions[online] 48 Continued Fractions and Pell’s Equation[online] 49 Generating Functions[9nline] 50 Sums of Powers [online] A Factorization of Small Composite Integers[online] B A List of Primes [online]
