Number Theory : $\gcd$ of $(a^2 + b^2, a+b)$ , where $\gcd$ of $(a,b)$ $ = $ $1$? I was solving some basic number theory problems when I came across :

What is $\gcd(a^2 + b^2, a+b)$, where $a$ and $b$ are relatively prime integers that are not both $0$?

Can someone help me out ? Even a hint , upon which I can build , would suffice ...

Hint Modulo $a+b$, $(a+b)^2\equiv 0$ so $a^2+b^2\equiv -2ab$. Hence you want to compute $(2ab,a+b)$. 
