1. The problem statement, all variables and given/known data Given gcd(a,b)=1, what is the gcd(a^2+b^2, a+b) where ^=square. 2. Relevant equations 3. The attempt at a solution gcd(a^2+b^2, a+b) = gcd ( (a+b)^2 -2ab, a+b) which i think, we can reduce to gcd(2ab, a+b). Here is where I stucked. I am not sure how to proceed. Please could anyone help me?