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Thread: Sum of fours and fives

  1. #1
    Senior Member I-Think's Avatar
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    Sum of fours and fives

    Prove, via induction or otherwise, that if $\displaystyle n\geq12,$ then n can be written as the sum of $\displaystyle 4's$ and $\displaystyle 5's$.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    $\displaystyle 12=4+4+4$
    $\displaystyle 13=4+4+5$
    $\displaystyle 14=4+5+5$
    $\displaystyle 15=5+5+5$
    $\displaystyle 16=4+4+4+4$
    ...........................
    ...........................
    Thus, if the number is a multiple of 4, it can be written as 4n

    If the number is of the form 4n+1, it can be written as 4(n-1)+5

    If the number is of the form 4n+2, it can be written as 4(n-2)+5*2

    If the number is of the form 4n+3, it can be written as 4(n-3)+5*3.
    Last edited by alexmahone; Jun 27th 2009 at 08:43 PM.
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