# Definition:Repunit

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## Definition

Let $b \in \Z_{>1}$ be an integer greater than $1$.

Let a (positive) integer $n$, greater than $b$ be expressed in base $b$.

$n$ is a **repunit base $b$** if and only if $n$ is a repdigit number base $b$ whose digits are $1$.

That is, $n$ is a **repunit base $b$** if and only if all of the digits of $n$ are $1$.

When $b$ is the usual base $10$, $n$ is merely referred to as a **repunit**.

### Index

The **index** of a **repunit** is the number of digits it has.

Thus a **repunit** with $n$ digits can be referred to as $R_n$.

## Also see

- Results about
**repunits**can be found here.

## Historical Note

According to David Wells, in his *Curious and Interesting Numbers* of $1986$, the term **repunit** was coined by Albert H. Beiler.

## Linguistic Note

The derivation of the term **repunit** is clear: it comes from **rep**eated **unit**.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $11$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $1,111,111,111,111,111,111$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): Glossary - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $11$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $1,111,111,111,111,111,111$