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): $11$