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Table of Content | Table of Contents1. What Is Number Theory?2. Pythagorean Triples3. Pythagorean Triples and the Unit Circle4. Sums of Higher Powers and Fermat?s Last Theorem5. Divisibility and the Greatest Common Divisor6. Linear Equations and the Greatest Common Divisor7. Factorization and the Fundamental Theorem of Arithmetic8. Congruences9. Congruences, Powers, and Fermat?s Little Theorem10. Congruences, Powers, and Euler?s Formula11. Euler?s Phi Function and the Chinese Remainder Theorem12. Prime Numbers13. Counting Primes14. Mersenne Primes15. Mersenne Primes and Perfect Numbers16. Powers Modulo m and Successive Squaring17. Computing kth Roots Modulo m18. Powers, Roots, and ?Unbreakable? Codes19. Primality Testing and Carmichael Numbers20. Squares Modulo p21. Is -1 a Square Modulo p? Is 2?22. Quadratic Reciprocity23. Proof of Quadratic Reciprocity24. Which Primes Are Sums of Two Squares?25. Which Numbers Are Sums of Two Squares?26. As Easy as One, Two, Three27. Euler?s Phi Function and Sums of Divisors28. Powers Modulo p and Primitive Roots29. Primitive Roots and Indices30. The Equation X4 + Y4 Z431. Square?Triangular Numbers Revisited32. Pell?s Equation33. Diophantine Approximation34. Diophantine Approximation and Pell?s Equation35. Number Theory and Imaginary Numbers36. The Gaussian Integers and Unique Factorization37. Irrational Numbers and Transcendental Numbers38. Binomial Coefficients and Pascal?s Triangle39. Fibonacci?s Rabbits and Linear Recurrence Sequences40. Oh, What a Beautiful Function41. Cubic Curves and Elliptic Curves42. Elliptic Curves with Few Rational Points43. Points on Elliptic Curves Modulo p44. Torsion Collections Modulo p and Bad Primes45. Defect Bounds and Modularity Patterns46. Elliptic Curves and Fermat?s Last Theorem47. The Topsy-Turvey World of Continued Fractions 48. Continued Fractions, Square Roots, and Pell?s Equation |
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