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
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 $\displaystyle n$