We consider a variant of Fermat's well-known equation xn+yn=zn. T his variant replaces the usual powers with the factorial powers defined by xn=x(x-1)...(x-(n-1)). For n=2 we characterize all possible integer solutions of the equation. For n=3 we show that there exist infinitely many non-trivial solutions to the equation. Finally we show there exists no maximum n for which xn+yn = zn has a non-trivial solution.

Author Bio

Matthew Green graduated with a B.Sc. in Mathematics from Towson University in 2011, where he completed this research during his senior year. He plans to attend graduate school in pursuit of a PhD in mathematics.