Greatest Common Divisor is in a set

label Algebra
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Show that if a, b (= Z such that a, b not= 0, then gcd(9a, 9b) = 9 ยท gcd(a, b). 

[Hint: Let d = gcd(a, b). Then show that the product 9d satisfies the definition of the GCD of 9a and 9b 

Mar 25th, 2015

d=gcd(a, b) if and only if then a = d*a' and b = d*b' where a' and b' are mutually prime integers.

Since 9a = (9d)*a' and 9b = (9d)*b', we conclude that 9d = gcd(9a, 9b).

Mar 25th, 2015

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Mar 25th, 2015
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