We will introduce the notion of automatic sequence and relate it to algebraicity of formal power series over finite field of rational functions. While doing this we will lay out the main ideas of Christol’s theorem which connects these two concepts. Furthermore, we will use these ideas to show if for prime \(p\) we have \(p \mid m\), then the Artin-Mazur zeta function \(\zeta_{x^m}(\overline{\mathbb{F}}_p;t) \in \mathbb{Q}(t)\), similarly if \(p \nmid m\), then \(\zeta_{x^m}(\overline{\mathbb{F}}_p;t)\) is transcendental over \(\mathbb{Q}(t)\).