Let $\displaystyle R$ be a Euclidean Domain. Let $\displaystyle m$ be the minimum integer in the set of norms of nonzero elements of $\displaystyle R$. Prove that every nonzero element of norm $\displaystyle m$ is a unit in $\displaystyle R$ . Deduce that a nonzero element of norm zero (if such an element exists) is a unit.