I want to know if this is correctly solved
Find (a:b) knowing that the remainder from dividing $a$ by $b$ is 27and the remainder from dividing $b$ by $27$ is $21$
So, $r_{b}(a) = 27$ and $r_{27}(b) = 21$
What I did is to use the gcd property that says that $(a:b) = (b:r_{b}(a))$
So, by this property, $(a:b) = (b:r_{b}(a)) = (b:27) = (27:r_{27}(b)) = (27:21) = 3$
Thanks