Prove that every integer greater than 11 can be expressed as the sum of 2 composite numbers.
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Originally Posted by JCIR Prove that every integer greater than 11 can be expressed as the sum of 2 composite numbers. If $\displaystyle n$ is even: $\displaystyle \tfrac{n}{2}+\tfrac{n}{2}$. If $\displaystyle n$ is odd: $\displaystyle 9 + (n-9)$. EDIT: Mistake on the even part.
Last edited by ThePerfectHacker; Jul 9th 2008 at 03:54 PM.
$\displaystyle 14 = \frac{{14}}{2} + \frac{{14}}{2} = 7 + 7\,?\,$ How about if n is even: $\displaystyle \left( {n - 4} \right) + 4$
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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