Question

For any positive integer n ,prove that nq-n is divisible by 6.

Answer 1

N³ - n = n(n²-1) = n(n -1)(n + 1) is divided by 3 then possible reminder is 0, 1 and 2 [ ∵ if P = ab + r , then 0 ≤ r < a by Euclid lemma ]