Recent content by automan13

TROGLIO thanks big time. I should have thought of factoring it. It becomes obvious from there. Thanks Again:smile:

Sorry, had a typo. 3 divides n^3 -n . Also i can't use induction. All we've learned so far is proof by cases, direct proof, contrapositive and contradiction.

1. For any integer n, prove that 3 divides n^3 -n The Attempt at a Solution I'm stuck. I understand that means that n^3 -n mod 3 =0. or I can n^3 -n can be expressed as 3x. But I don't know how to prove it. Where do i go from here. Thanks