An integer $n$ is represented by the binary quadratic form $a x^{2}+b x y+c y^{2}$ if there exist integers $r$ and $s$ such that $n=a r^{2}+b r s+c s^{2} .$ Discriminant is defined as: $d:=b^{2}-4 a c .$
There is a well-known property that says: an integer $n$ is represented (in fact, properly) by some binary quadratic form of discriminant $d$ if and only if $d$ is a square mod $4 n .$
I was wondering if there is an analogous result for quadratic forms in more than two variables, I have looked for references but I have not been successful in finding it.
Thanks for your time.
