A friendly introduction to number theory

 Content: 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. 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  Index  *44. The Topsy-Turvey World of Continued Fractions [online]  *45. Continued Fractions, Square Roots, and Pell's Equation [online]  *46. Generating Functions [online]  *47. Sums of Powers [online]  *A. A List of Primes [online]  *These chapters are available online.