  We prove that for every digraph $F$ and every assignment of pairs of integers
$(r_e,q_e)_{e \in A(F)}$ to its arcs there exists an integer $N$ such that
every digraph $D$ with dichromatic number at least $N$ contains a subdivision
of $F$ in which $e$ is subdivided into a directed path of length congruent to
$r_e$ modulo $q_e$, for every $e \in A(F)$.
  This generalizes to the directed setting the analogous result by Thomassen
for undirected graphs, and at the same time yields a novel short proof of his
result.
