Question: 3. Let a, b E Z, not both zero, let d = god(a, b), and let k be any non-zero integer. (a) By referring to

3. Let a, b E Z, not both zero, let d = god(a, b), and let k be any non-zero integer. (a) By referring to the definition of divisibility at the very beginning of Section II- 1 of the course notes, show that kd divides both ka and kb. (b) By using the G.C.D. Theorem, show conversely that if an integer e divides both ka and kb, then e divides kd. (c) Deduce that god(ka, kb) = [k| ged(a, b)

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