Combinatorics and number theory have been intrinsically connected to topology since its origins with Euler's polyhedral formula. Polyhedral products have remarkably illustrated this connection by exploring the combinatorial properties of simplicial complexes and the topology of their corresponding moment-angle complexes. In this talk, and motivated by Coxeter's genus formula, we will discuss how the topology of some moment-angle complexes and the canonical action of the simplicial automorphism group of the underlying simplicial complex. encode nice arithmetic identities and solve combinatorial problems, thus opening the door to applications of polyhedral products in number theory.