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- #1

- Jan 26, 2012

- 995

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**Problem**: Show that $n^{13}-n$ is divisible by $2730$ for all $n$.

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**Note**: This is equivalent to showing that $n^{13}-n\equiv 0\pmod{2730}$ for all $n$.

**Hint**:

Use Fermat's theorem coupled with the Chinese Remainder Theorem to show this result.

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