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

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- Aug 29th 2006, 09:18 AMnortonKMProof 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 - Aug 29th 2006, 09:56 AMGlaysher
Suppose $\displaystyle n$ is even

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

Suppose $\displaystyle n$ is odd

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

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