3.I.9G

Let $f(x, y)=a x^{2}+b x y+c y^{2}$ be a binary quadratic form with integer coefficients. Explain what is meant by the discriminant $d$ of $f$. State a necessary and sufficient condition for some form of discriminant $d$ to represent an odd prime number $p$. Using this result or otherwise, find the primes $p$ which can be represented by the form $x^{2}+3 y^{2}$.

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