Prove that $\gcd(a + a', b + b') = 1$ if $ab - a'b' = \pm 1$
My attempt was:
Case 1:
$ab - a'b' = 1 \implies \gcd(a, b') = 1$ and $\gcd(a', b) = 1$
Then is it sufficient to conclude that $\gcd(a + a', b + b') = 1$?
Furthermore, when we write $\pm 1$, does it mean or
or and
?
Thanks,