periodic generating function

[Kevin Ryde <user42_kevin@yahoo.com.au>]

To notice a periodic part in a generating function I think I want to
find whether a denominator polynomial is a divisor of 1 - C*x^p, for
some constant C and some power p.  What would be a good way to do that?

I got the effect I wanted by working upwards determining successive
terms of quotient until only a high term (or stop if too long).
Coefficients might be complex or quad and I'm happy for C to be
likewise.