# Definition:Kaprekar Triple

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## Definition

Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Suppose that $n^3$, when expressed in number base $b$, can be split into three parts that add up to $n$.

Then $n$ is a Kaprekar triple for base $b$.

### Sequence of Kaprekar Triples

The sequence of Kaprekar triples begins:

$1, 8, 45, 297, 2322, 2728, 4445, 4544, 4949, 5049, 5455, 5554, \ldots$

## Examples

### 45

$45$ is a Kaprekar triple.

### 297

$297$ is a Kaprekar triple.

## Source of Name

This entry was named for Dattathreya Ramchandra Kaprekar.