# Move yourself to four years back!

An integer $$x$$ is selected at random between $$\displaystyle 1$$ and $$2011!$$. The probability that $$x^{x}-1$$ is divisible by 2011 can be expressed in the form $$\dfrac{m}{n}$$ where $$m$$ and $$n$$ are positive coprime numbers. Find the value of $$m$$.

Details and Assumptions

You may use the fact that 2011 is prime.

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