Solution
= Solution
The <continued fraction convergents> of $\sqrt{67}$ begin $8,41/5,90/11,131/16,221/27$. The last one yields
$$
\boxed{x=221,\qquad y=27,\qquad 221^2-67\cdot27^2=48841-48843=-2.}
$$
Changing either sign gives another valid <integer> solution.