Around the p-adic Littlewood Conjecture

In this dissertation, we look at the Littlewood Conjecture and several related open problems. We introduce notions and theorems from various fields in order to properly formulate the conjectures and properly state the various results related to them. In Chapter 5, we investigate a potential counter-example to the p-adic Littlewood conjecture when p=2 via an intricate construction, and show that this potential counter-example does indeed satisfy the premises of the conjecture.