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.
Green, Matthew J.
"A Factorial Power Variation of Fermat's Equation,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 13
, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol13/iss1/3