(Solved): 6) Show that the product of any two, three, four, or five consecutive positive integers is never a ...

6) Show that the product of any two, three, four, or five consecutive positive integers is never a perfect square. (It is true that no product on n >= 2 consecutive positive integers is a square (P. Erd¨os, 1935). Moreover, no such a product is even a perfect m >= 2 power (Erd¨os-Selfridge, 1975).)