4. Try to find a set of positive integer solutions for the equation $x^{2}-51 y^{2}=1$.

Translate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.
$$
\text { Hint: } \begin{aligned}
x^{2} & =51 y^{2}+1 \\
& =49 y^{2}+14 y+1+2 y^{2}-14 y \\
& =(7 y+1)^{2}+2 y(y-7) .
\end{aligned}
$$

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