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You are not logged in. #1 20060405 09:56:29
GCD ProofsGiven this theorem: #2 20060405 11:55:36
Re: GCD ProofsTo prove it's unique, let d = gcd(a, b), and then assume there is another gcd, e. It should be fairly easy from here, because one property of the gcd is that it is the greatest common divisor of a and b. Can you have two greatests? "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20060405 11:58:51
Re: GCD ProofsFor the second one, you use the fact that if d = gcd(a, b) and n = ax + by for some n in Z, then d  n. It should be straightforward from there. Last edited by Ricky (20060405 11:59:18) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #4 20060405 12:10:39
Re: GCD ProofsThanks! The book is called "Introduction to Abstract Mathematics", the class is titled "Intro to logic for secondary mathematics". Thanks for all your help.. i took this class as an elective thinking it would be easier than most of the other upper level math classes, but its turned into a real pain in the math. 