Category:Number times Recurring Part of Reciprocal gives 9-Repdigit

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Let a (strictly) positive integer $n$ be such that the decimal expansion of its reciprocal has a recurring part of period $d$ and no non-recurring part.

Let $m$ be the integer formed from the $d$ digits of the recurring part.

Then $m \times n$ is a $d$-digit repdigit number consisting of $9$s.