Definition:Niven Number
From ProofWiki
Definition
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:
- $\displaystyle \exists A \in \Z: N = \sum_{k=0}^m r_k b^k = A \sum_{k=0}^m r_k$
where $\displaystyle \sum_{k=0}^m r_k b^k$ is the representation of $N$ in base $b$ as defined according to the Basis Representation Theorem.
Also see
Source of Name
This entry was named for Ivan Morton Niven.
