  We give an explicit algebraic description, based on prismatic cohomology, of
the algebraic K-groups of rings of the form $O_K/I$ where $K$ is a p-adic field
and $I$ is a non-trivial ideal in the ring of integers $O_K$; this class
includes the rings $\mathbf{Z}/p^n$ where $p$ is a prime.
  The algebraic description allows us to describe a practical algorithm to
compute individual K-groups as well as to obtain several theoretical results:
the vanishing of the even K-groups in high degrees, the determination of the
orders of the odd K-groups in high degrees, and the degree of nilpotence of
$v_1$ acting on the mod $p$ syntomic cohomology of $\mathbf{Z}/p^n$.
