Problem
Let $P_n(x) = 1 + \dfrac{1}{2}x - \dfrac{1}{8}x + \cdots + (-1)^n \dfrac{1.3.5 \cdots (2n - 3)}{2.4.6 \cdots 2n}x^n$ Prove that if $\alpha = 8y + 1$ and $\alpha \geq 3$, then $P_{\alpha - 3}(8y)^2$ is a solution to $x^2 \equiv a \pmod{2^\alpha}$.
I'm really confused about that notation. Is $P_{\alpha - 3}(8y)^2 = P_{\alpha - 3}(64y^2) \text{ or } P^2_{\alpha - 3}(8y) ?$
Thanks