Math 5336 Number Theory Dr. Cordero
Class activities for November 18, 2002
Topic: Number Theoretic Functions
- Given a positive integer n, let denote the number of positive divisors on n and denote the sum of these divisors.
- For any arbitrary real number x, we denote by [x] the largest integer less than or equal to x; that is, [x] is the unique integer satisfying x-1 <[x] < x.
2. Compute for each given n:
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
§ Find by means of the formula given in Theorem 6.2:
§ 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.