- #1
chan8366
- 3
- 0
Homework Statement
prove:6 divides (n^3-n) for all integers n.
Homework Equations
n^3-n=(n)(n+1)(n-1)
The Attempt at a Solution
tried to use direct proof. Then used cases that involed n=2k for some integer k and n=2k+1 for some integer k. However, i could not get it so that 6 was factored from either odd/even of n^3-n i.e. n^3-n=6m for some integer m.
Just a hint please.