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
- Weisstein, Eric W. "Brown Numbers." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BrownNumbers.html