Hi, I am currently stuck on this sequence question, I tried playing around with it for a while now, can't seem to solve it. Any help would be appreciated!

What are a necessary and sufficient set of conditions on these integer sequences $\displaystyle \{a_n\}_{n \ge 0}$ and $\displaystyle \{b_n\}_{n \ge 0}$ in order to satisfy the equation $\displaystyle A(x) \times B(x) = 1$ for all $\displaystyle x \in \mathbb{R}$ such that $\displaystyle A(x), B(x)$ are defined. Where $\displaystyle A(x) = a_0+a_1x+a_2x^2+ \cdots$ and $\displaystyle B(x) = b_0+b_1x+b_2x^2+ \cdots$

Thanks again!