A student, named Daniel Reichman, asked this question. Suppose that a,b, and c, integers, satisfy a^2+b^2= c^2. For which n are there a,b such that 2ab=n! ? He notes that there are at least three solutions: For n=4, a=4, b=3 For n=5 a=12, b=5 For n=6, a=40, b=9 Are there any other such n?