A Friendly Introduction to Number Theory, 4/e (IE-Paperback)

Joseph H. Silverman

  • 出版商: Prentice Hall
  • 售價: $1,300
  • 貴賓價: 9.8$1,274
  • 語言: 英文
  • 頁數: 432
  • 裝訂: Paperback
  • ISBN: 0321782364
  • ISBN-13: 9780321782366

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<內容簡介>

 

  • Preface

  • Flowchart of Chapter Dependencies

  • Introduction

  • 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. Is -1 a Square Modulo p? Is 2?

  • 22. Quadratic Reciprocity

  • 23. Proof of Quadratic Reciprocity

  • 24. Which Primes Are Sums of Two Squares?

  • 25. Which Numbers Are Sums of Two Squares?

  • 26. As Easy as One, Two, Three

  • 27. Euler’s Phi Function and Sums of Divisors

  • 28. Powers Modulo p and Primitive Roots

  • 29. Primitive Roots and Indices

  • 30. The Equation X4 + Y4 = Z4

  • 31. 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 p

  • 44. Torsion Collections Modulo p and Bad Primes

  • 45. Defect Bounds and Modularity Patterns

  • 46. Elliptic Curves and Fermat’s Last Theorem

  • Further Reading

  • Index

  • *47. The Topsy-Turvey World of Continued Fractions [online]

  • *48. Continued Fractions, Square Roots, and Pell’s Equation [online]

  • *49. Generating Functions [online]

  • *50. Sums of Powers [online]

  • *A. Factorization of Small Composite Integers [online]

  • *B. A List of Primes [online]