\begin{definition}[Definition:Digital Root]
Let $n \in \Z: n \ge 0$.
Let $n$ be expressed in base $b$ notation.
Let $n_1 = \map {s_b} n$ be the digit sum of $n$ to base $b$.
Then let $n_2 = \map {s_b} {n_1}$ be the digit sum of $n_1$ to base $b$.
Repeat the process, until $n_m$ has only one digit, that is, that $1 \le n_m < b$.
Then $n_m$ is the '''digital root of $n$ to the base $b$'''.
\end{definition}