Def/Euclidean algorithm

=Termination= We prove here that the Euclidean algorithm eventually terminates, so that the sequences $(q_k)$ and $(r_k)$ are finite as stated before.

In order to see that the Euclidean algorithm eventually terminates (so that the sequences $(q_k)$ and $(r_k)$ are finite as stated), it suffices to observe that $r_k = 0$ for some $k \in \NN$. Indeed, consider the

=Examples= The following are examples of the Euclidean algorithm: