Definition:Brown Numbers

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Definition

Brown numbers are pairs of integers $\left({m, n}\right)$ such that:

$n! + 1 = m^2$

There are only $3$ known such pairs:

$\left({5, 4}\right)$
$\left({11, 5}\right)$
$\left({71, 7}\right)$


Also see


Linguistic Note

The origin of the term Brown numbers is currently unclear.

It is supposed that they may be named after a mathematician, but research will be needed to establish which one.


It is understood that there is no association with the urban industrial street definition for the term brown numbers: numbers which are made up as you go along, in order to support a deliberately fallacious argument or false statement: literally brown, because you've just pulled them out of your arse.


Sources