Norm form equations and linear divisibility sequences

Abstract: 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. We show that in some cases, these sequences are linear divisibility sequences.

number theory

Audience: researchers in the topic

Number Theory Online Conference 2020