Linear Recurrence Sequences in Diophantine Analysis

Diophantine analysis is an area of number theory concerned with finding integral solutions to polynomial equations defined over the rationals, or more generally over a number field. In some cases, it is possible to associate a well behaved recurrence sequence to the solution set of a Diophantine equation, which can be useful in generating explicit results. It is known that the solution set to any norm form equation is naturally associated to a family of linear recurrence sequences. As these sequences have been widely studied, Diophantine problems involving norm forms are well-suited to be studied through their associated sequences. In this dissertation, we use this method to study two such problems