# Math Help - Contradiction proof

Prove n is odd if and only if n^3 is odd. So we want to prove if n is odd then n^3 is not odd. Which is the contradiction.

If n is odd then there exist a number in which n=2m+1. Where do I go from here to finish the proof?

2. ok, e n is odd and $n^3$ is even. By def of odd and even, there
$\exists \: m \in \mathbb{Z}$ such that $n = 2m + 1$ similarly, $\exists \: k \in \mathbb{Z}$ such that $n^3 = 2k$ so $(2m+1)^3 = 2k$ if you remember what division meant, if a divides b then there exists an integer g such that b = ag. since k is an integer, this means 2 divides (2m+1)^3 which means 2 divides (2m+1) which is a contradiction.