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Math Help - Number Theory

  1. #1
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    Wink Number Theory

    Prove that every integer greater than 11 can be expressed as the sum of 2 composite numbers.
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  2. #2
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    Quote Originally Posted by JCIR View Post
    Prove that every integer greater than 11 can be expressed as the sum of 2 composite numbers.
    If n is even: \tfrac{n}{2}+\tfrac{n}{2}.
    If n is odd: 9 + (n-9).

    EDIT: Mistake on the even part.
    Last edited by ThePerfectHacker; July 9th 2008 at 03:54 PM.
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  3. #3
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    14 = \frac{{14}}{2} + \frac{{14}}{2} = 7 + 7\,?\,

    How about if n is even: \left( {n - 4} \right) + 4
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  4. #4
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    I propose this solution:

    Write the number as one of the following:
    3n + 4
    3n + 6
    3n + 8
    (where n > 1).

    Hence
    12 = 6 + 6
    13 = 9 + 4
    14 = 6 + 8
    15 = 9 + 6
    16 = 12 + 4
    17 = 9 + 8
    etc.
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