Definition:EPORN

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.