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Why are the only numbers $m$ for which $n^{m+1}\equiv n \pmod{m}$ is true also unique for $\displaystyle\sum_{n=1}^{m}{n^m}\equiv 1 \bmod m$?
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Why are the only numbers $m$ for which $n^{m+1}\equiv n \pmod{m}$ also the only numbers such that $\displaystyle\sum_{n=1}^{m}{n^m}\equiv 1 \bmod m$?
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