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.