Week 5-Lecture 23 : Euler ๐œ‘-function - I

Lecture 24 of 50 in Number Theory by NPTEL IIT Bombay. 38 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 ยท 9 min
  2. Week 1-Lecture 1 : Integers ยท 30 min
  3. Week 1-Lecture 2 : Divisibility and primes ยท 32 min
  4. Week 1-Lecture 3 : Infinitude of primes ยท 23 min
  5. Week 1-Lecture 4 : Division algorithm and the GCD ยท 31 min
  6. Week 1-Lecture 5 : Computing the GCD and Euclidโ€™s lemma ยท 28 min
  7. Week 2-Lecture 6 : Fundamental theorem of arithmetic ยท 29 min
  8. Week 2-Lecture 7 : Stories around primes ยท 28 min
  9. Week 2-Lecture 8 : Winding up on `Primes' and introducing `Congruences' ยท 28 min
  10. Week 2-Lecture 9 : Basic results in congruences ยท 31 min
  11. Week 2-Lecture 10 : Residue classes modulo n ยท 30 min
  12. Week 3-Lecture 11 : Arithmetic modulo n, theory and examples ยท 33 min
  13. Week 3-Lecture 12 : Arithmetic modulo n, more examples ยท 28 min
  14. Week 3-Lecture 13 : Solving linear polynomials modulo n - I ยท 30 min
  15. Week 3-Lecture 14 : Solving linear polynomials modulo n - II ยท 30 min
  16. Week 3-Lecture 15 : Solving linear polynomials modulo n - III ยท 31 min
  17. Week 4-Lecture 16 : Solving linear polynomials modulo n - IV ยท 31 min
  18. Week-Lecture 17 : Chinese remainder theorem, the initial cases ยท 29 min
  19. Week 4-Lecture 18 : Chinese remainder theorem, the general case and examples ยท 31 min
  20. Week 4-Lecture 19 : Chinese remainder theorem, more examples ยท 31 min
  21. Week 4-Lecture 20 : Using the CRT, square roots of 1 in โ„คn ยท 36 min
  22. Week 5-Lecture 21 : Wilson's theorem ยท 29 min
  23. Week 5-Lecture 22 : Roots of polynomials over โ„คp ยท 31 min
  24. Week 5-Lecture 23 : Euler ๐œ‘-function - I ยท 38 min
  25. Week 5-Lecture 24 : Euler ๐œ‘-function - II ยท 30 min
  26. Week 5-Lecture 25 : Primitive roots - I ยท 30 min
  27. Week 6-Lecture 26 : Primitive roots - II ยท 29 min
  28. Week 6-Lecture 27 : Primitive roots - III ยท 29 min
  29. Week 6-Lecture 28 : Primitive roots - IV ยท 27 min
  30. Week 6-Lecture 29 : Structure of Un - I ยท 30 min
  31. Week 6-Lecture 30 : Structure of Un - II ยท 28 min
  32. Week 7-Lecture 31 : Quadratic residues ยท 29 min
  33. Week 7-Lecture 32 : The Legendre symbol ยท 32 min
  34. Week 7-Lecture 33 : Quadratic reciprocity law - I ยท 26 min
  35. Week 7-Lecture 34 : Quadratic reciprocity law - II ยท 29 min
  36. Week 7-Lecture 35 : Quadratic reciprocity law - III ยท 29 min
  37. Week 7-Lecture 36 : Quadratic reciprocity law - IV ยท 32 min
  38. Week 8-Lecture 37 : The Jacobi symbol ยท 27 min
  39. Week 8-Lecture 38 : Binary quadratic forms ยท 27 min
  40. Week 8-Lecture 39 : Equivalence of binary quadratic forms ยท 27 min
  41. Week 8-Lecture 40 : Discriminant of a binary quadratic form ยท 28 min
  42. Week 8-Lecture 41 : Reduction theory of integral binary quadratic forms ยท 30 min
  43. Week 9-Lecture 42 : Reduced forms up to equivalence - I ยท 28 min
  44. Week 9-Lecture 43 : Reduced forms up to equivalence - II ยท 27 min
  45. Week 9-Lecture 44 : Reduced forms up to equivalence - III ยท 29 min
  46. Week 9-Lecture 45 : Sums of squares - I ยท 28 min
  47. Week 9-Lecture 46 : Sums of squares - II ยท 30 min
  48. Week 9-Lecture 47 : Sums of squares - III ยท 35 min
  49. Week 10-Lecture 48 : Beyond sums of squares - I ยท 28 min
  50. Week 10-Lecture 49 : Beyond sums of squares - II ยท 28 min