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9. Let a, b, q be positive integers, and r be an integer with 0 ≤...

9. Let a, b, q be positive integers, and r be an integer with 0 ≤ r < b. (a) Explain why gcd(a, b) = gcd(b, a). (b) Prove that gcd(a, 0) = a. (c) Prove that if a = bq + r, then gcd(a, b) = gcd(b, r).

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