QUOTE(Elnendil @ Oct 3 2010, 03:33 AM)
So what is your issue? Post a counterproof, something else. I guess i'm sounding overly harsh here, but suddenly you're dismissing the concept and i'm wanting to know the details and some sort of counterproof that works so I can retract the statement.
I'm not. I don't know what you're saying anymore. I was pointing out that 1 is a valid GCD, since you said it had "no GCD" if the algorithm gave you 1. I have no idea where you're going with the "lower common divisor". If you want to prove that no other number can be the GCD, you'd have to prove that there's no BIGGER divisor.
Also, a|b means "a divides b". I'm not sure if you're saying otherwise.
By the way, it's valid up to a unit (i.e. a divisor of 1) or something like that. Probably. I'd have to think about it.