1. NUMBER THEORY Chapter 1: The Integers

2. The Well-Ordering Property.

3. example Finite set – {1,2,3,4,5} – {2,4,6,7,15} – {101, 10001, 100001, 11, 111} Infinite set – {1,3,5,7,9,11,…} – {1,1,2,3,5,8,13,21,34,…}

4. Divisibility.

6. divisors

11. Linear Combination

14. Exercise If 7| 21 and 7|49, suggest 3 more integers divisible by 7.

15. Division Algorithm

17. More exercise

18. More examples

19. More example

20. More examples

22. Prime Numbers

25. Lemma (?)

27. How many Primes?

33. GREATEST COMMON DIVISOR

34. Greatest Common Divisor

35. Example

36. Relatively Prime

38. Example No common factor other than 1.

42. Linear Combination

44. Bezout’s theorem If a and b are integers, then there are integers m and n such that ma+nb=(a,b).

45. Corollary a and b are relatively prime if and only if there is integers a and b, ma+nb=1.

46. Interesting result a and b are relatively prime if and only if there is integers a and b, ma+nb=1. (na, nb)=n (a,b)

47. More examples

54. EUCLIDEAN ALGORITHM Number Theory

57. Example

58. Extended Euclidean Algorithm

59. FUNDAMENTAL THEOREM OF ARITHMETIC Integers

64. Greatest Common Divisor

71. LINEAR DIOPHANTINE EQUATION Integers