1. The problem statement, all variables and given/known data Prove by Contradiction: For all integers x greater than 11, x equals the sum of two composite numbers. 2. Relevant equations A composite number is any number that isn't prime To prove by contradiction implies that if you use a statement's as a negation, a contradiction arises 3. The attempt at a solution The negation of the original statement is: There exists an integer x such that if x > 11, then x does not equal the sum of two composite numbers. I'm really stuck on this one, I tried substituting in values using the quotient remainder theorem (a number can be represented as 2r, or 2r + 1.. or alternatively 3r, 3r + 1, or 3x + 2, but I wasn't getting anywhere with it). Some direction would be appreciated!