Title: The connection between Diophantine equations and binary trees
Abstract: Binary trees are used to encode a lot of different types of information and can be used to make decisions by following different paths along the tree. It turns out you can also use these trees to represent the different possible 2-adic valuations for sequences like $x^2+D.$ Further, these valuation trees allow us to look at Diophantine equations of the form $x^2+D=2^cy$, $y$ odd, and determine the possible solutions. The goal of this talk is to share how to use binary trees to create valuation trees and then use those trees to determine the possible integer solutions of specific Diophantine equations.