I don't get it - what to assume in the following problem for solving by induction
Prove that 6 divides n^3 - n whenever n is a nonnegative integer
I tried following:
assume for "k" --
k^3 - k = 6r for some integer "r"
now to prove "k+1" we get:
(k+1)^3 - (k+1) = k^3 + 3k^2+3k+1 - k - 1
= (k^3-k) +3k^2+3k
= 6r + 3k^2+3k by induction
what should i do after this? I am not getting "6" as a common factor how come 6 divides n^3-n!!!