Question 84
If $a$ is a positive integer less than $100$, for how many values of $a$ does the system
$$
\begin{cases}
x^{2} = y + a \\
y^{2} = x + a
\end{cases}
$$
have integer solutions?
$$
\begin{cases}
x^{2} = y + a \\
y^{2} = x + a
\end{cases}
$$
have integer solutions?