Norm Form Equations and Linear Divisibility Sequences

Finding integer solutions to norm form equations is a classic Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It turns out that such a sequence can be written as a tuple of integer linear recurrence sequences, each with characteristic polynomial equal to the minimal polynomial of our unit. After an expository introduction to norm form equations and linear recurrence sequences, I will plan to discuss how one might use this observation to investigate when these sequences satisfy a certain divisibility property. This is ongoing work with few preliminary results, so comments and questions are especially encouraged.