The rational fraction
a, c, p, q positive integers, reduces to a polynomial under conditions specified in a result of Grosswald who also stated necessary and sufficient conditions for all the coefficients to tie nonnegative.
This last result is given a different proof using lemmas interesting in themselves.
The method of proof is used in order to give necessary and sufficient conditions for the positive coefficients to be equal to one. For a < 2pq, a = αp + βq, α, β nonnegative integers, c > 1, the exact positions of the nonzero coefficients are established. Also a necessary and sufficient condition for the number of vanishing coefficients to be minimal is given.