
quadratic forms
Consider a quadratic form $\displaystyle f(x,y) = ax^2 + bxy + cy^2$ with $\displaystyle a,b,c \in \mathbb{Z}$ and discriminant $\displaystyle D = b^2  4ac$
We know that f factors as a product of linear forms $\displaystyle (ux+vy)(u'x+v'y)$ with rational coefficients if and only if D is a square.
Under which conditions for $\displaystyle a,b,c$ are $\displaystyle u,v,u',v' \in \mathbb{Z}$?

You might want to use Gauss's Lemma.

I don't get Gauss lemma and I don't see how to use it here.