A proof involving Greatest common divisors
Now you have ca and cb. you get cr from jeffreydk's hint.
Then you have cb and cr, which implies cgcd(b,r), which means c is a common divisor of b and r.
if c=gcd(a,b), you are supposed to show c is actually the GREATEST common divisor of b and r
here's another way, gcd(a,b)gcd(b,r) and gcd(b,r)gcd(a,b) will imply they are equal. I think you have already got gcd(a,b)gcd(b,r), you can prove gcd(b,r)gcd(a,b) in a similar way.
