Question

Show that n^3 - n is divisible by 8, if n is an odd positive integer.

Answer 1

Answer:

As n^3-n can be written as (n-1)(n)(n+1)

So it denotes three consecutive integers with n as odd and remaining two as even and the product of 2 even positive integers is always divisible by 8 so the given expression is always divisible by 8.