## Problem of the Day #171: Periodic Powers in Base 10
*September 6, 2011*

*Posted by Albert in : potd , trackback*

Let $S$ = $\{0,1,\ldots,9\}$.

Some $k = 1$ is trivially interesting because the set of the last digit of [each element of $S$ taken to the $k^{\text{th}}$ power] is a permutation of $S$. Find the $171^{\text{th}}$ highest $k$ for which this property holds.

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