Power series as a Euclidean domain

Question

I must prove that the ring of formal power series $\mathbb{R} [[x]]$ is a Euclidean domain.

So I started and I think I should start with for each nonpower series $P$, define $f(P)$ as degree of the smallest power of $x$ occurring in $P$. In particular, for two nonzero power series $P$ and $Q$, $f(P) < f(Q)$ iff $P$ divides $Q$.

Answer 1

Hint: It's a DVR since it's got a unique maximal ideal which is principally generated.