3. Let three positive integers $a$, $x$, $y$ greater than 100 satisfy $y^{2}-1=a^{2}\left(x^{2}-1\right)$.
Find the minimum value of $\frac{a}{x}$.
3. Notice that,
$$
\begin{array}{l}
y^{2}=a^{2} x^{2}-a^{2}+1100, a=2 x, y=2 x^{2}-1 \text{ all satisfy the conditions.} \\
\text{Thus, the minimum value of } \frac{a}{x} \text{ is 2.}
\end{array}
$$