Find the values of for which is a Square Number , where is the Factorial (Brocard 1876, 1885). The only known solutions are , 5, and 7, and there are no other solutions . The pairs of numbers are called Brown Numbers.

**References**

Brocard, H. Question 166. *Nouv. Corres. Math.* **2**, 287, 1876.

Brocard, H. Question 1532. *Nouv. Ann. Math.* **4**, 391, 1885.

Guy, R. K. *Unsolved Problems in Number Theory, 2nd ed.* New York: Springer-Verlag, p. 193, 1994.

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1999-05-26