Repunit is Zuckerman Number
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Theorem
Let $n$ be a repunit.
Then $n$ is also a Zuckerman number.
Proof
The digits of a repunit are by definition all $1$.
Thus the product of the digits of a repunit is $1$.
By One Divides all Integers, $1$ is a divisor of $n$.
Hence the result, by definition of Zuckerman number.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $11$