Counting homomorphisms between cyclic groups is a common exercise in a first
course in abstract algebra. A similar problem, accessible at the same level, is
to count the number of group homomorphisms from a dihedral group of order $2m$
into a dihedral group of order $2n$. While the solution requires only
elementary group theory, the result does not appear in the literature or in the
usual texts. As the solution may be of interest, particularly to those teaching
undergraduate abstract algebra, it is provided in this note.
