Determine $\gcd (a + b, a^2− b^2)$ where integers $a + b$ and $a^2− b^2$ are not both zero.
We can rewrite $a^2 - b^2$ as $(a+b)(a-b)$. So $a+b$ is a factor of $a^2 - b^2$.
In case $a+b$ is negative, we can ensure positivity by taking the modulus $\lvert a+b \rvert$.
So
$$ \gcd \; (\; a + b \; , \; a^2− b^2 \;) = \lvert a+b \rvert$$