(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

prove:6 divides (n^3-n) for all integers n.

2. Relevant equations

n^3-n=(n)(n+1)(n-1)

3. 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.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Math proof

**Physics Forums | Science Articles, Homework Help, Discussion**