Prove that given $a,b \in \mathbb{Z} : \gcd(a,b)=1 \Rightarrow \exists s,t : sa+tb=1$
Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$