# Power series $f$ s.t. $f(\zeta_{p^n}-1)=1/p^n$ for allmost all $n \geq 0$.
Let $p$ be a prime number and $\zeta_{p^n}$ a primitive $p^n$-th root of unity. Find $f \in \mathbf Q_p[[X]]$ fulfilling $f(\zeta_{p^n}-1)=1/p^n$ for all sufficiently large $n$.