Repunit is Zuckerman Number

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): $11$
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