This book, which needs to be returned quite soon, has a problem I don't know where to start. How do I find a 4 parameter solution to the equation
The title of the section this problem comes from is entitled (as this question is titled) "Numbers of the Form $x^2+axy+by^2$", yet it deals almost exclusively with numbers of the form $x^2+y^2$. It looks like almost an afterthought or a preview of what's to come where it gives the formula
Then 6 of the 7 problems use this form. The first few involve solving the form $z^k=x^2+axy+by^2$, which I quickly figured out are solved by letting $z=u^2+auv+bv^2$, then using the above formula to get higher powers. So for $z^2$ for example, I set $m=p=u$ and $n=q=v$ to get $x$ and $y$ in terms of $u$ and $v$. But for this problem, I'm drawing a blank.