209. Solve the equation $x^{2}-11 y=4$ in integers.
209. $\frac{x^{2}-4}{11}=y$; we directly verify that when $x= \pm 2$, the number $x^{2}-4$ is divisible by 11; therefore, $x=11 t \pm 2$, $y=t(11 t \pm 4)$. Thus, the integer solutions of the given equation are contained in the formulas

$$
\left\{\begin{array}{l}
x=11 t \pm 2 \\
y=t(11 t \pm 4)
\end{array}\right.
$$

where the plus-minus signs correspond.