Suppose,
$ P(x) := \sum_{n\geqslant r} {p_{n}x^n}$ and $ Q(x) := \sum_{n\geqslant s} {q_{n}x^n} $
are formal power series, where $p_{r}$ and $q_{s}$ doesnt equal $0$ such that $x^r$ is the smallest-order non-zero term of P(x) and $x^s$ is the lowest for Q(x).
By a Corollary stating: Let R(x) and S(x) be a formal power series. If the constant term of S(x) is non-zero, then there is a formal power-series C(x) such that $ S(x)C(x) = R(x) $ thus the solution A(x) is unique
From the corollary, $s=0$ is an okay condition such that Q(x)C(x) = P(x) to have a solution. I need to give a necessary condition for Q(x)C(x) = P(x) to have a solution, and prove that it is right. Also when a solution exists, is it unique?
Any hints to show how i can have a condition for this equation to have a solution?