# Math Help - Proof Question

1. ## Proof Question

Hi,

I have been trying to solve this problem but I cannot figure out a way to solve it.

Show that: For every n in Z+, n can be written as the power of 2 and an odd integer.

Thanks

2. Suppose $n$ is even

Then $n = 2^0 + (n - 1)$ where $n - 1$ is odd

Suppose $n$ is odd

Suppose positive integer $x \ne 0$ is such that $2^x < n$

Then $2^x$ is even and you need to add an odd number to get equal to $n$