CMI sub-question

If \(a\) is an element in the set \(\{2,3,4,\ldots,9999\}\), there are two values that a can take such that \(a^2-a\) is divisible by 10000. Find the absolute difference between these two values.

As a bonus, can you find the number of such values of \(a\) for a general set \(\{2,3,\ldots,(n^2-1)\}\), for any positive integer \(n\)?

Note that I do not know the answer to the bonus question. I made a mistake in the exam hall.

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