  Our main result is elementary and concerns the relationship between the
multiplicative groups of the coordinate and endomorphism rings of the formal
additive group over a field of characteristic $p>0$. The proof involves the
combinatorics of base $p$ representations of positive integers in a striking
way. We apply the main result to construct a canonical quotient of the module
of Coleman power series over the Iwasawa algebra when the base local field is
of characteristic $p$. This gives information in a situation which apparently
has never previously been investigated.
