Working modulo 11

#group_theory

Let $n$ be a number between $0$ and $10$ . Compute $n^{111} (\mod 11)$ , expressing your answer as a number between $0$ and $10$ . Give as detailed a proof as you can, justifying every step, no matter who trivial you think it is.

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Let $n$ be a number between $0$ and $10$. Compute $n^{111}\pmod{11}$, expressing your answer as a number between $0$ and $10$. Give as detailed a proof as you can, justifying every step, no matter who trivial you think it is.