4-163 Find any set of positive integers $x$ and $y$ that satisfy the equation $x^{2}-51 y^{2}=1$.

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[Solution] The original equation can be transformed into
$$
x^{2}=(7 y+1)^{2}+2 y(y-7) \text {, }
$$

Let $y=7$, we get $x=50$.
Therefore, $x=50, y=7$ is a positive integer solution to the original equation.