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# hw6 - (15 points 3 Let a = 6468 and b = 44590(a Compute...

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CSCI 2011: Homework 6 Due: April 9, 2010 before class. No late submissions. This assignment must be completed individually, on your own. The homework contains 7 questions worth 100 points total. You can solve the bonus question to get extra credit of up to 15 points. You must obtain at least 50 points to pass this homework. When answering questions, always justify your answer. The exercises below are from the 6 th edition of Rosen. 1. Prove or disprove: (a) if a b (mod m) and a c (mod m), then a b + c (mod m) (7 points) (b) if a b (mod m), then 2a 2b (mod 2m) (8 points) 2. Section 3.6 Problem 20 on page 230. Show intermediate steps.
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Unformatted text preview: (15 points) 3. Let a = 6468 and b = 44590 (a) Compute gcd(a,b) using the prime factorizations of a and b (5 points) (b) Compute gcd(a,b) using Euclidean algorithm. Show intermediate steps. (5 points) 4. Section 4.1 Problem 4 on page 279 (Parts a, b, c, d, f: 2 points, part e: 5 points. Total 15 points) 5. Section 4.1 Problem 32 on page 280 (11 points) 6. Section 4.1 Problem 50 on page 281 (17 points) 7. Section 4.2 Problem 14 on page 292 (17 points) Extra Credit Question: Section 3.6 Problem 30 on page 230 (15 points) Hint: 10 -1 (mod 11)...
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