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Let a, b, c 2 Z+.
(a) Prove that if a|b, then ac|bc for all c.
(b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
(c) Prove that gcd(a, a + b) = gcd(a, b).
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1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.
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