Integers as the sum of 3 integers.

[cragar]

Homework Statement

Prove that every integer >17 can be written as the sum of 3 integers >1 that are pairwise relatively prime.

The Attempt at a Solution

I already proved the case for even integers. Now I am just working on the case for odd integers.
I know that it has to be the sum of 3 odd integers because it can't be the sum of 2 even and one odd. I started with 2x+1=x+(x+1) where x is a positive integer. now either x or x+1 is even and I guess I could break the even one up as a sum of 2 odd numbers and then go from their.

 

[mfb]

The proof (as an explicit construction of those 3 integers) for odd integers can be done similar to the proof for even integers, just with more casework.

 

[lurflurf]

Did you finish the one about Prove that every integer >6 can be written as the sum of 2 integers >1 that are pairwise relatively prime? It is the same idea consider n/3-1,n/3,n/3+1 and adjust slightly in different cases.