1. The problem statement, all variables and given/known data Prove that every integer bigger than 6 can be written as a sum of 2 integers bigger than 1 which are relatively prime. 3. The attempt at a solution Ill first look at the case where our number is odd. Let x be an odd integer. I will just add (x-2)+2=x since x is odd so is x-2 and 2 is even so x-2 and 2 are relatively prime. Now Lets look at the case where our number 2y is even. and y is even. 2y=y+y=(y+1)+(y-1) now since y is even y+1 and y-1 are odd. and y-1 and y+1 are odd numbers separated by a factor of 2. Lemma 1: Let n be an odd number. Lets assume for contradiction that n and[itex] n+2^x [/itex] have a common factor so it should divide their difference but [itex]n+2^x-n=2^x[/itex] but n and [itex]n+2^x [/itex] do not have a factor of 2 because they are odd. so y+1 and y-1 are relatively prime by lemma 1. Now lets look at the case where 2z=z+z where z is odd. we will just look at 2z=z+z=(z+2)+(z-2) since z is odd z-2 and z+2 are odd and they are odd numbers separated by a power of 2 so they are relatively prime.