1. Consider the sets $A=\left\{x_{n} \mid x_{n}=1 \cdot 2 \cdot 3 \cdot \ldots \cdot n+57, n \in \mathbb{N}^{*}\right\}$ and $B=\left\{y^{4} \mid y \in \mathbb{N}\right\}$.

a) Prove that $x_{9} \notin B$.

b) Determine the set $A \cap B$.