Brown Numbers

Brown numbers are Pairs $(m,n)$ of Integers satisfying the condition of Brocard's Problem, i.e., such that

$$n!+1=m^2$$

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 Erdös conjectured that these are the only three such Pairs.

See also Brocard's Problem, Factorial, Square Number, Wilson Prime

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.