Thread: prove

Prove that if d s a positive integer, d/a and d/b, then gcd(a,b)=d iff
gcd(a/d,b/d)=1

Originally Posted by mandy123

Prove that if d s a positive integer, d/a and d/b, then gcd(a,b)=d iff
gcd(a/d,b/d)=1

this is straightforward..

and a/d and b/d are both integers since d|a and d|b

Originally Posted by kalagota

and a/d and b/d are both integers since d|a and d|b

The following addendum to kalagota's answer is probably obvious, but just in case: implies that , so that since conversely and imply .