Question

Let a,b be integers and d=gcd(a,b). Show that gcd(a/d,b/d)=1

Answer 1

by what methods?

Answer 2

You have d=gcd(a,b). By the GCD characterization theorem this means there exists integers x and y so that ax+by = d. Now what happens when you divide both sides of the equation by d?

Answer 3

i was hoping for that method lol

Answer 4

(a/d)x+(b/d)y=1 where a/d = a and b/d = b? therefore gcd(a/d, b/d) = 1 ?

Answer 5

(a/d)x+(b/d)y=1 is correct but how did you get a/d =a and b/d = b ?