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 December 30th, 2014, 04:18 PM #1 Senior Member   Joined: Dec 2006 Posts: 167 Thanks: 3 Is there infinite many k such that (k+1) | 10^k-1 ? Suppose $k,\,d\in\mathbb{N}^+$. Prove or disprove: Set $\{k : (k+1 \mid 10^k -1)\wedge \big(((0 < d< k)\wedge (d \mid k))\implies (k+1\nmid 10^d -1)\big)\}$ is not finite.

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