\begin{definition}[Definition:Niven Number]
A '''Niven number''' (in a given number base $b$) is a positive integer which is divisible by the sum of its digits in that given base $b$.
That is, $N$ is a '''Niven number base $b$''' {{iff}}:
:$\ds \exists A \in \Z: N = \sum_{k \mathop = 0}^m r_k b^k = A \sum_{k \mathop = 0}^m r_k$
where $\ds \sum_{k \mathop = 0}^m r_k b^k$ is the representation of $N$ in base $b$ as defined according to the Basis Representation Theorem.
\end{definition}