Math 5336 Number Theory                                                                     Dr. Cordero

 

Class activities for November 11,  2002

Topic: Fermatís Little Theorem; Eulerís Theorem

Divisibility Tests for Bases Other than Ten

 

A. Review Homework from last time:

        Page 133 # 1, 5, 6.

        Handout # 1-27 odd

 

B. The Lockers problem

 

C. Inverse Theorem: There is an integer x such that (mod m) if and only

gcd(a, m)=1.

 

D. Cancellation Theorem: If gcd(a, m)=1 and (mod m), then (mod m).

 

E. Fermatís Little Theorem: If p is prime and gcd(a, p)=1, then (mod p).

 

F. Corollary: If p is prime, then (mod p) for every integer a.

 

G. Eulerís Theorem: If gcd(a, m)=1, then (mod m).

 

H. Divisibility Tests for Bases Other than Ten (Back of page)