Can (2) Be Proved Without Knowing (1)?

[annoymage]

Homework Statement

(1). If gcd(a,b) = d , gcd(a/d,b/d)=1

(2). If gcd(a,b) = d , then gcd(m,n) = 1 , where dm=a, dn=b
(i don't know wether this statement is correct)

Homework Equations

n/a

The Attempt at a Solution

i kow how to prove (1) and (2), but i only proof (2) using (1), my professor applying that (2) without us knowing what (1) is. seeming that they are other direct and obvious ways for proving (2),
so is there any? i can't see T_T

 

[HallsofIvy]

(1) and (2) says exactly the same thing. The same proof will work for both.