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## Problem of the Day #315: Divisibility into $99 \ldots 99900 \ldots 000$January 28, 2012

Posted by Albert in : potd , trackback

Thanks to my dad for this problem.

Prove (or find a counterexample) that given a positive integer $n$, $\exists \quad i,j: \quad n \mid (10^i – 1)(10^j)$.

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