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3. Prove that gcd(a, b) = gcd(3a +56, 11a +186), for any integers a and b. 4. Homework. Suppose gcd(ab, c) = 1. Prove that abc | d if, and only if ab | d and c | d.

3. Prove that gcd(a, b) = gcd(3a +56, 11a +186), for any integers a and b. 4. Homework. Suppose gcd(ab, c) = 1. Prove that abc | d if, and only if ab | d and c | d.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Just solve question 4 only (homework)
1. Suppose gcd(a, b) = 1. Prove that ab | c if, and only if a | c and b|c. 2. Prove that for integers a and b, gcd(a, a + b) = gcd(b, a - b). 3. Prove that gcd(a, b) = ged(3a + 5b, 11a + 18b), for any integers a and b. 4. Homework. Suppose gcd(ab, c) = 1. Prove that abc | d if, and only if ab | d and c | d.
Transcribed Image Text:1. Suppose gcd(a, b) = 1. Prove that ab | c if, and only if a | c and b|c. 2. Prove that for integers a and b, gcd(a, a + b) = gcd(b, a - b). 3. Prove that gcd(a, b) = ged(3a + 5b, 11a + 18b), for any integers a and b. 4. Homework. Suppose gcd(ab, c) = 1. Prove that abc | d if, and only if ab | d and c | d.
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