(a) Show that there are exactly 2 numbers $a$ in $\{2, 3, \ldots, 9999\}$ for which $a^2 - a$ is divisible by 10000. Find these values of $a$.\\
(b) Let $n$ be a positive integer. For how many numbers $a$ in $\{2, 3, \ldots, n^2 - 1\}$ is $a^2 - a$ divisible by $n^2$? State your answer suitably in terms of $n$ and justify.