Question: What is the solution to exercise Exercise . 1. If a and b are integers, not both of which are zero, verify that god(a, b)

What is the solution to exercise

Exercise . 1. If a and b are integers, not both of which are zero, verify that god(a, b) = god(-a, b) = god(a, -b) = god(-a, -b). 2. Prove that, for a positive integer n and any integer a, god(a, a + n) divides n. Then show god(a, a + 1) = 1. 3. Given integers a and b, prove the following: (a) There exist integers a and y for which c = ax + by if and only if god(a, b) |c. (b) If there exist integers a and y for which ax + by = god(a, b), then god(x, y) = 1. 4. For any integer a, show the following: (a) god(2a + 1, 9a + 4) = 1. (b) god(5a + 2, 7a + 3) = 1. (c) If a is odd, then god(3a, 3a + 2) = 1

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