# Factoring numbers “of the (binary quadratic) form” in two different ways

For some fixed $n$ define the quadratic form $$Q(x,y) = x^2 + n y^2.$$

I think that if $Q$ represents $m$ in two different ways then $m$ is composite.

I can prove this for $n$ prime. I was hoping someone could give me a hint towards proving this result for general $n$? Also would be interested in generalizations if any are known! Thanks a lot.

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