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 If $d= \gcd(a+b,a^2+b^2)$, then $d\mid(a-b)(ab)$ hence
$$d \mid (a^2+b^2) \pm (a^2-b^2)$$
