If $u\equiv 1$ mod $m$ and $n$ any natural number $\neq$ char$(K)$, then $u$ is a $n$-th power in $K$.

34 Views Asked by At

let $k$ be a complete, non-Archimedean field, $R$ the corresponding valuation ring, $m$ its maximal ideal. If $u\equiv 1$ mod $m$ and $n$ any natural number $\neq$ char$(K)$, then $u$ is a $n$-th power in $K$.

I am stuck at the condition $u\equiv 1$ mod $m$. What does it mean?