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Thread: Proof Question

  1. #1
    nortonKM
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    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
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  2. #2
    Member Glaysher's Avatar
    Joined
    Aug 2006
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    Newton-le-Willows
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    224
    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 $\displaystyle n$
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