Math 5336 Number Theory Dr. Cordero
Class activities for September 23, 2002
Topic: Divisibility Theory in the Integers, III
· Practice: §2.1 pp 19-20 # 1, 2, 3a, 3b.
· (Part 5) What is the statement for integers that are relatively prime?
3. Continue with handout from last time:
6. a. Question: If a|b and b|c, must ab|c? Study some cases.
b. Prove the following theorem:
Theorem If a|c and b|c with gcd(a,b)=1, then ab|c.
7. a. Question: If a|bc, must a|b and a|b?
b. If a|bc with gcd(a,b)=1, must a|c?
8. Practice: §2.2 p.25 # 7, 14
9. Euclidean Algorithm: Read page 27 (up to Lemma ).
· What is the Euclidean Algorithm?
· What is the Euclidean Algorithm used for?
· Write an example where you use the Euclidean Algorithm.
10. a. Find gcd(364, 140).
b. How can we write gcd(364, 140) as a linear combination of 364 and 140?
11. Use the Extended Euclidean Algorithm to find integers x and y such that:
12. The Stamps Problem
Suppose you have an unlimited supply of 6 -cents stamps and 11- cents stamps.
What amounts of postage can you make with these stamps?
· Solve the Stamps problem.
· What if the stamps were of 6-cents and 9-cents?
· What if the stamps were of 6-cents and 10-cents?