I was reading a Proof that stated
Since $\gcd(a, b) = 1$, it follows that $\gcd(ab, a^2 + b^2) = 1$.
I can't figure out why this statement is true. I tried to factor $ab$ and $a^2+b^2$, but I don't think that you can really reduce $a^2$ and $b^2$ because it's just addition. I'm not really sure how to go about this. Any help?