I've been stuck on these two problems from my problem set for quite a while. Any help would be appreciated!
2)Suppose that $ax^2 + bxy + xy^2$ is equivalent to $Ax^2 + Bxy + Cy^2$. Show that $gcd (a, b, c) = gcd (A, B, C)$?
3)Let $f(x, y) = ax^2 + bxy + cy^2$ be a positive semidefinite quadratic form of discriminant 0. Put $g = gcd (a, b, c)$. Show that f is equivalent to the form $gx^2$.