Let $p$ be a prime number, let $n\in \mathbb{N}$. Then the $n$-th $p$-adic Witt polynomial is defined by

$w_n(X):=\sum_{d|n}d X_d^{n/d}$

This formula comes out of consideration of addition of Teichmüller representatives?, a multiplicative section of the natural projection $A\to k$ of a discrete valuation ring to its residue field?. This section is unique if $k$ is perfect.

Witt polynomials are one way to define Witt vectors.