Show that every integer greater than 11 is the sum of two composite integers.
Do I need to use induction for this question? I've tried, but it's not working.

Here's my work so far:

Let P(n): n=a+b for n>11, where a and b are composite integers.

Initial step: P(12) says that 12 is the sum of two composite integers because 12=4+8=6+6 where 4, 6 and 8 are all composite integers.

Induction step: Let k>11 and suppose P(k) is true and k=a+b.

We want to show that P(k+1) is true.

k+1=a+b+1

this is what i've tried, but actually I'm not sure if I'm on the right track. Just give me some suggestions. Thanks very much !!!