Math 5336 – Number Theory Day 11 Class activities for November 11,  2002

Dr. Cordero

Topics: Fermat’s Little Theorem; Euler’s Theorem
Divisibility Tests for Bases Other than Ten

  1. Review Homework from last time:
    • Page 133 # 1, 5, 6.
    • Handout # 1-27 odd
  2. The Lockers problem
  3. Inverse Theorem: There is an integer x such that (mod m) if and only gcd(a, m)=1
  4. Cancellation Theorem: If gcd(a, m)=1 and (mod m), then  (mod m).
  5. Fermat’s Little Theorem: If p is prime and gcd(a, p)=1, then  (mod p).
  6. Corollary: If p is prime, then (mod p) for every integer a.
  7. Euler’s Theorem: If gcd(a, m)=1, then  (mod m).
  8. Divisibility Tests for Bases Other than Ten (Back of page)
    ********           HOMEWORK: READ SECTION 6.4           ******