[Aurelius]

There are several ways. Easiest is to take the (alternating) series for 1/e (= 1/2! - 1/3! + 1/4! - ...) and multiply through by n!, for any arbitrary n. Then after multiplication the first (n-1) terms are integers and the remaining terms add to a number with magnitude less than 1. So n!/e is not an integer for any n.

[AmishDude]

Works for me.