Consider quadratic form $$Q(w,x,y,z)=w^2-x^2-y^2+z^2$$ and fix $r\in(0,\frac12)$ and pick a large enough $n\in\Bbb N$.
How do we find a solution to $$Q(w,x,y,z)\bmod n=0$$ on condition that $$\sqrt n\log n\leq \min(x,z)<\max(x,z)<\min(w,y)<\max(w,y)\leq2\sqrt n\log n$$ $$n^{r}\leq\min(w-x,y-z)<\max(w-x,y-z)\leq 2n^{r}$$ for without using exhaustive search?
