Joseph H.Silverman拥有哈佛大学博士学位。他目前为布朗大学数学教授,之前曾任教于麻省理工学院和波士顿大学。1998年,他获得了美国数学会Steele奖的著述奖,获奖著作为《TheArithmetic of Elliptic Curves》和《Advanced Topics in the Arithmeticof Elliptic Curves》。 他的研究兴趣是数论、椭圆曲线和密码学等。
【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 Powe and Fermat’S Last Theorem 5 Divisibility and the Greatest Common Divisor 6 Linear Equatio and the Greatest Common Divisor 7 Factorization and the Fundamental Theorem ofArithmetic 8 Congruences 9 Congruences,Powe ,andFermat’S LittleTheorem 10 Congruences,Powe ,and Euler’S Formula 11 Euler’S Phi Function and the Chinese Remainder Theorem 12 Prime Numbe 13 Counting Primes 14 Me enne Primes 15 Me enne Primes and Perfect Numbe 16 Powe Modulo m and Successive Squaring 17 Computing kth Roots Modulo m 18 Powe ,Roots,and“Unbreakable Codes l9 Primality Testing and Carmichael Numbe 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 Squares 25 Which Numbe Are Sums ofTwo Squares 26 As Easy as One,TwO,Three 27 Euler’S Phi Function and Sums of Diviso 28 Powe Modulo р and Primitive Roots 29 Primitive Roots and Indices 30 The Equation X4+Y4=Z 3l Square-Triangular Numbe Revisited 32 Pell’S Equation 33 Diophantine Approximation 34 Diophantine Approximation and Pell’S Equation 35 Number Theory and Imaginary Numbe 36 The Gaussian Intege and Unique Factorization 37 Irrational Numbe and Tra cendental Numbe 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 To ion Collectio Modulo р and Bad Primes 45 Defect Bounds and Modularity Patter 46 Elliptic Curves and Fermat’S Last Theorem Further Reading Index 47 The Topsy-Turvy World of Continued Fractio [online] 48 Continued Fractio and Pell’s Equation[online] 49 Generating Functio [9nline] 50 Sums of Powe [online] A Factorization of Small Composite Intege [online] B A List of Primes [online]
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