/sci/ - Science & Math

Anyone who knows number theory and quadratic congruences give me a quick hand here.

I am looking at the problem in pic related and I have a problem with pic related. You see, they refer to theorem 6 which says:

If p divides [math] x^2 - Dy^2 [/math] and gcd(x,y) = 1 then D is a quadratic residue mod p

The problem is that they are applying the theorem, but I see no guarantee of x and y being relatively prime. The problem says that x and y could be any numbers, not necessarily relatively prime. So how come they can just assume x and y are relatively prime and apply theorem 6 like its nothing? What am I not seeing.