Prove that $H_m \mid R_{6m}$, where $H_m = 10^{2m} - 10^m + 1$ and $R_{6m}$ is a repunit.
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We want to show that $H_m \mid R_{6m}$, which is equivalent to showing that $R_{6m} = k H_m$ for some integer $k$. Show more…
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