The following is a question in my textbook:
Show that any positive definite binary quadratic form of discriminant $-3$ is equivalent to $f(x, y) = x^2 + xy + y^2$. Show that a positive integer $n$ is properly represented by $f$ if and only if $n$ is of the form $n = 3^\alpha \prod p^\beta$, where $\alpha = 0$ or $1$ and all primes are of the form $3k + 1$. Show that for $n$ of this form, the number of proper representations is $6 \cdot 2^s$ where $s$ is the number of distinct primes $p = 1 \mod 3$ that divide $n$.
However, I have no idea where to begin. It was mentioned that we could use Eisenstein integers like Gaussian integers in the similar proof of binary quadratic forms of discriminant -3, but I'm still stuck.
I know how to prove the first statement.