# Proof Question

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• August 29th 2006, 09:18 AM
nortonKM
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
• August 29th 2006, 09:56 AM
Glaysher
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 $n$