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Let $f(x,y)=(ex+fy)(gx+hy); \ x,y,e,f,g,h \in \mathbb{Z}$ be a reducible integral binary quadratic form. Is there a criterion to determine if a number is represented by this form? In particular, does such a criterion exist for if an integral binary quadratic form has square discriminant?

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  • $\begingroup$ Prime factorization, or Gauss's Disquisitiones. $\endgroup$
    – Franz Lemmermeyer
    Commented Aug 1, 2017 at 22:13

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