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Math Help - Proof Question

  1. #1
    nortonKM
    Guest

    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
    Posts
    224
    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
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