# Definition:EPORN

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## Definition

An **EPORN** is a natural number which can be expressed as the product of a number and its reversal in two different ways.

## Examples

### Example: $2520$

The smallest EPORN is $2520$:

\(\ds 2520\) | \(=\) | \(\ds 210 \times 012\) | ||||||||||||

\(\ds \) | \(=\) | \(\ds 120 \times 021\) |

### Example: $63 \, 504$

The number $63 \, 504$ is the smallest EPORN which is not a multiple of $10$:

\(\ds 63 \, 504\) | \(=\) | \(\ds 441 \times 144\) | ||||||||||||

\(\ds \) | \(=\) | \(\ds 252 \times 252\) |

### Example: $144 \, 648$

The EPORN $144 \, 648$ does not include a palindrome:

\(\ds 144 \, 648\) | \(=\) | \(\ds 861 \times 168\) | ||||||||||||

\(\ds \) | \(=\) | \(\ds 492 \times 294\) |

## Also see

- Results about
**EPORNs**can be found here.

## Historical Note

**EPORNs** appear to have been first investigated by Shyam Sunder Gupta, who first published on the subject in $1987$.

This work has been reported on in a few outlets since.

## Linguistic Note

The word **EPORN** is an acronym formed from ** Equal Product Of Reversible Number**.

The term appears to have been coined by Shyam Sunder Gupta, who has investigated them in some detail.

## Sources

- February 1987: S.S. Gupta:
*EPORNS*(*Science Today (India)*)