1. ## Number Theory

Prove that every integer greater than 11 can be expressed as the sum of 2 composite numbers.

2. Originally Posted by JCIR
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.

3. $14 = \frac{{14}}{2} + \frac{{14}}{2} = 7 + 7\,?\,$

How about if n is even: $\left( {n - 4} \right) + 4$

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.