Week 2-Lecture 6 : Fundamental theorem of arithmetic

Lecture 7 of 50 in Number Theory by NPTEL IIT Bombay. 29 min. Watch on YouTube

Course: Number Theory (Mathematics). Covers: primes divisibility modular arithmetic congruences diophantine.

All lectures in Number Theory

  1. Course Introduction A basic course in number theory · 9 min
  2. Week 1-Lecture 1 : Integers · 30 min
  3. Week 1-Lecture 2 : Divisibility and primes · 32 min
  4. Week 1-Lecture 3 : Infinitude of primes · 23 min
  5. Week 1-Lecture 4 : Division algorithm and the GCD · 31 min
  6. Week 1-Lecture 5 : Computing the GCD and Euclid’s lemma · 28 min
  7. Week 2-Lecture 6 : Fundamental theorem of arithmetic · 29 min
  8. Week 2-Lecture 7 : Stories around primes · 28 min
  9. Week 2-Lecture 8 : Winding up on `Primes' and introducing `Congruences' · 28 min
  10. Week 2-Lecture 9 : Basic results in congruences · 31 min
  11. Week 2-Lecture 10 : Residue classes modulo n · 30 min
  12. Week 3-Lecture 11 : Arithmetic modulo n, theory and examples · 33 min
  13. Week 3-Lecture 12 : Arithmetic modulo n, more examples · 28 min
  14. Week 3-Lecture 13 : Solving linear polynomials modulo n - I · 30 min
  15. Week 3-Lecture 14 : Solving linear polynomials modulo n - II · 30 min
  16. Week 3-Lecture 15 : Solving linear polynomials modulo n - III · 31 min
  17. Week 4-Lecture 16 : Solving linear polynomials modulo n - IV · 31 min
  18. Week-Lecture 17 : Chinese remainder theorem, the initial cases · 29 min
  19. Week 4-Lecture 18 : Chinese remainder theorem, the general case and examples · 31 min
  20. Week 4-Lecture 19 : Chinese remainder theorem, more examples · 31 min
  21. Week 4-Lecture 20 : Using the CRT, square roots of 1 in ℤn · 36 min
  22. Week 5-Lecture 21 : Wilson's theorem · 29 min
  23. Week 5-Lecture 22 : Roots of polynomials over ℤp · 31 min
  24. Week 5-Lecture 23 : Euler 𝜑-function - I · 38 min
  25. Week 5-Lecture 24 : Euler 𝜑-function - II · 30 min
  26. Week 5-Lecture 25 : Primitive roots - I · 30 min
  27. Week 6-Lecture 26 : Primitive roots - II · 29 min
  28. Week 6-Lecture 27 : Primitive roots - III · 29 min
  29. Week 6-Lecture 28 : Primitive roots - IV · 27 min
  30. Week 6-Lecture 29 : Structure of Un - I · 30 min
  31. Week 6-Lecture 30 : Structure of Un - II · 28 min
  32. Week 7-Lecture 31 : Quadratic residues · 29 min
  33. Week 7-Lecture 32 : The Legendre symbol · 32 min
  34. Week 7-Lecture 33 : Quadratic reciprocity law - I · 26 min
  35. Week 7-Lecture 34 : Quadratic reciprocity law - II · 29 min
  36. Week 7-Lecture 35 : Quadratic reciprocity law - III · 29 min
  37. Week 7-Lecture 36 : Quadratic reciprocity law - IV · 32 min
  38. Week 8-Lecture 37 : The Jacobi symbol · 27 min
  39. Week 8-Lecture 38 : Binary quadratic forms · 27 min
  40. Week 8-Lecture 39 : Equivalence of binary quadratic forms · 27 min
  41. Week 8-Lecture 40 : Discriminant of a binary quadratic form · 28 min
  42. Week 8-Lecture 41 : Reduction theory of integral binary quadratic forms · 30 min
  43. Week 9-Lecture 42 : Reduced forms up to equivalence - I · 28 min
  44. Week 9-Lecture 43 : Reduced forms up to equivalence - II · 27 min
  45. Week 9-Lecture 44 : Reduced forms up to equivalence - III · 29 min
  46. Week 9-Lecture 45 : Sums of squares - I · 28 min
  47. Week 9-Lecture 46 : Sums of squares - II · 30 min
  48. Week 9-Lecture 47 : Sums of squares - III · 35 min
  49. Week 10-Lecture 48 : Beyond sums of squares - I · 28 min
  50. Week 10-Lecture 49 : Beyond sums of squares - II · 28 min