作(編/譯)者 : SILVERMAN 出版年份 : 2014 ISBN : 9781292027098 書號 : BX0145N 幾色 : 1 規格 : 平裝 發行公司 : PEARSON 英文書名中譯 : 數論學 版次 : 4E 頁數 : 480 Table of Contents: 1. What Is Number Theory? 2. Pythagorean Triples 3. Pythagorean Triples and the Unit Circle 4. Sums of Higher 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 of Arithmetic 8. Congruences 9. Congruences, Powers, and Fermat’s Little Theorem 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 19. Primality Testing and Carmichael Numbers 20. Squares Modulo p 21. Quadratic Reciprocity 22. Proof of Quadratic Reciprocity 23. Which Primes Are Sums of Two Squares? 24.Which Numbers Are Sums of Two Squares? 25. Euler’s Phi Function and Sums of Divisors 26. Powers Modulo p and Primitive Roots 27. Primitive Roots and Indices 28. The Equation X4 + Y4 = Z4 29. Square–Triangular Numbers Revisited 30. Pell’s Equation 31. Diophantine Approximation 32. Diophantine Approximation and Pell’s Equation 33. Number Theory and Imaginary Numbers 34. The Gaussian Integers and Unique Factorization 35. Irrational Numbers and Transcendental Numbers 36. Binomial Coefficients and Pascal’s Triangle 37. Fibonacci’s Rabbits and Linear Recurrence Sequences 38. Cubic Curves and Elliptic Curves 39. Elliptic Curves with Few Rational Points 40. Points on Elliptic Curves Modulo p 41. Torsion Collections Modulo p and Bad Primes 42. Defect Bounds and Modularity Patterns 43. Elliptic Curves and Fermat’s Last Theorem 44. The Topsy-Turvy World of Continud Fractions 45. Continued Fractions and Pell’s Equation 46. Generating Functions 47. Sums of Powers 48. Appendix: A List of Primes