# 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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