\begin{definition}[Definition:Repdigit Number]
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 '''repdigit base $b$''' {{iff}} all of the digits of $n$ are the same digit.
For example:
:$55555$
or:
:$3333_4$
that second one being in base 4.
\end{definition}