Math 5336 Number Theory                                                                Dr. Cordero

 

Class activities for November 18,  2002

Topic: Number Theoretic Functions

 

1.      Definitions:

2. Compute  for each given n:

         n=75

         n=99

         n=243

         n=1024

3. What do you think  is, given that p and q are distinct primes?

    What do you think  is, given that p and q are distinct primes?

    What is ?

    What is ?

 

4. Study Theorem 6.1 Formula to obtain all the positive divisors of an integer n

                Theorem  6.2  Formulas for  and

                 Theorem 6.3   If gcd(a, b)=1, then  and                                                                                                 

 

3. Practice:

         Find  by means of the formula given in Theorem 6.2:

1.      n=75

2.      n=900

3.      n=6961

4.      n=17,640

         Page 109 # 5a

         Page 109 # 7a: Prove that  is an odd integer if and only if n is a perfect square.

                                                                             

4. An application to the calendar: Read 6.4. Then do Problems # 1, 2, 3, 5, 6.