Brown numbers are pairs of integers satisfying the
condition of Brocard's problem , i.e., such that

where
is the factorial and is a square number . Only
three such pairs of numbers are known: (5, 4), (11, 5),
(71, 7), and Erdős conjectured that these are the only three such pairs .

See also Brocard's Problem ,

Factorial ,

Square Number ,

Wilson
Prime
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References Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 193,
1994. Pickover, C. A. Keys
to Infinity. New York: Wiley, p. 170, 1995. Referenced on
Wolfram|Alpha Brown Numbers
Cite this as:
Weisstein, Eric W. "Brown Numbers." From
MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/BrownNumbers.html

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