Brown Numbers

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


where n! is the factorial and m^2 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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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.

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