Quadratic Mathematics | Part IB, 2003

Let f(x,y)=ax2+bxy+cy2f(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 dd of ff. State a necessary and sufficient condition for some form of discriminant dd to represent an odd prime number pp. Using this result or otherwise, find the primes pp which can be represented by the form x2+3y2x^{2}+3 y^{2}.

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