4 Try to find a set of positive integer solutions for the equation $x^{2}-51 y^{2}=1$
$$\begin{array}{l}
\text { Hint: } x^{2}=51 y^{2}+1 \\
=49 y^{2}+14 y+1+2 y^{2}-14 y \\
=\left(7 y+1\right)^{2}+2 y(y-7) \\
\end{array}$$

Let $y=7$. Then $x=50$