1. ## 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

2. 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..

$ax + by = d \Longleftrightarrow (a/d)x + (b/d)y = 1$ and a/d and b/d are both integers since d|a and d|b

3. Originally Posted by kalagota
$ax + by = d \Longleftrightarrow (a/d)x + (b/d)y = 1$ 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: $ax + by = d$ implies that $\gcd(a,b)|d$, so that $\gcd(a,b)=d$ since conversely $d|a$ and $d|b$ imply $d|\gcd(a,b)$.