- #1

FreshUC

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Prove that If the gcd(a,b) = c then c^2 divides ab

I know it looks very simple and it seems to be true, But I get the feeling I'm doing something wrong here in my proof. Would appreciate it if someone can explain if I'm on the right track or not.

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Proof by Contradiction:

Assume that gcd(a,b) = c and c^2 does not divide ab

Let a = 6 and b = 9. So,

gcd(6,9) = 3

ab = 54

c^2 = 9

But 54/9 = 6, so 9 divides 54 and therefore c^2 divides ab. This contradicts the assumption, so the claim "If gcd(a,b) = c then c^2/ab" is infact true.

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