我喜欢这本书。它讲解清晰，易于理解。用数值进行试验，用自己的方式从观察结果中猜测，最后完成证明。
　　——Jurgen Bierbrauer, 密歇根理工大学
　　本书每一章非常简短而且自成体系，很容易从中挑选我喜爱的主题。本书写作风格独特，书中提供了极佳的示例，以引出定理的叙述和证明。这种风格非常适合于数论的初级课程。
　　——Maureen Fenrick, 明尼苏达州立大学曼凯托分校

　　本书面向非数学专业学生，讲述了有关数论的知识，教给他们如何用数学方法思考问题，同时介绍了目前数学研究的前沿课题。本书采用轻松的写作风格，并包括大量数值示例。对于定理的证明，则强调证明方法而不仅仅是得到特定的结果。

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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 Numbers8
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. Euler’s Phi Function and Sums of Divisors
21. Powers Modulo p and Primitive Roots
22. Primitive Roots and Indices
23. Squares Modulo p
24. Is —1 a Square Modulo p? Is 2?
25. Quadratic Reciprocity
26. Which Primes Are Sums of Two Squares?
27. Which Numbers Are Sums of Two Squares?
28. The Equation X4 + Y 4 = 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. Oh, What a Beautiful Function
39. The Topsy-Turvy World of Continued Fractions
40. Continued Fractions, Square Roots and Pell’s Equation
41. Generating Functions
42. Sums of Powers
43. Cubic Curves and Elliptic Curves
44. Elliptic Curves with Few Rational Points
45. Points on Elliptic Curves Modulo p
46. Torsion Collections Modulo p and Bad Primes
47. Defect Bounds and Modularity Patterns
48. Elliptic Curves and Fermat’s Last Theorem Further Reading
A. Factorization of Small Composite Integers
B. A List of Primes
Index