Let $K$ be a number field and $v$ be it's one of $K$'s non-archimedian valuation. Then, I would like to prove $K_v(a^{1/m}) /K_v$ is unramified if only if $v(a)≡0 \pmod m$. This is from Silverman's 'the arithmetic of elliptic curves', p213. I know unramified extension of local field is in bij...