Suppose $d$ is a common divisor of two numbers $a_0$ and $a_1$, can $d$ be written as a linear combination of $a_0$,$a_1$ with integer coefficients? i.e. there exists two integers $i_0,i_1 \in \Bbb Z$ st. $d=i_0a_0+i_1a_1$.
I know this is true if $d$ is the greatest common divisor, see http://sites.millersville.edu/bikenaga/abstract-algebra-1/euclid/euclid.html. But I don't know if it holds if $d$ is just a common divisor. Can anyone give a proof or provide a counter example?