A Friendly Introduction to Number Theory, 4/e (IE-Paperback)
暫譯: 友善的數論入門（第4版，IE-平裝本）

<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 k^th 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]