Number Theory

Number Theory

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3 5 Computer Programming

12 of 37

12 of 37

3 5 Computer Programming

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Number Theory

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  1. 1 0 Introduction
  2. 2 1 1 The Principle of Mathematical Induction
  3. 3 1 2 The Basis Representation Theorem
  4. 4 2 1 The Division Algorithm
  5. 5 2 2a Divisibility
  6. 6 2 2b The Euclidean Algorithm
  7. 7 2 3 Linear Diophantine Equations
  8. 8 2 4 The Fundamental Theorem of Arithmetic
  9. 9 3 1 Permutations and Combinations
  10. 10 3 2 Fermat's Little Theorem
  11. 11 3 3 Wilson's Theorem
  12. 12 3 5 Computer Programming
  13. 13 4 1 Basic Properties of Congruences
  14. 14 4 2 Residue Systems
  15. 15 5 1 Linear Congruences
  16. 16 5 2 Fermat's Little Theorem and Wilson's Theorem
  17. 17 5 3 The Chinese Remainder Theorem
  18. 18 6 1a The Euler Phi Function Part 1
  19. 19 6 1b The Euler Phi Function Part 2
  20. 20 6 2 6 3 Multiplicative Functions
  21. 21 6 4 The Mobius Inversion Formula
  22. 22 7 1 Orders of Elements
  23. 23 7 2 Primitive Roots Modulo p
  24. 24 8 1 The Prime Counting Function
  25. 25 9 1 Euler's Criterion
  26. 26 9 2 The Legendre Symbol
  27. 27 9 3a Quadratic Reciprocity Part 1
  28. 28 9 3b Quadratic Reciprocity Part 2
  29. 29 9 4 Applications of Quadratic Reciprocity
  30. 30 10 1 Consecutive Residues
  31. 31 10 2a Consecutive Triples of Residues Part 1
  32. 32 10 2b Consecutive Triples of Residues Part 2
  33. 33 11 1 Sums of Two Squares
  34. 34 11 2 Sums of Four Squares
  35. 35 15 1 Gauss' Circle Problem
  36. 36 15 2 Dirichlet's Divisor Problem
  37. 37 Infinity Conclusion

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