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Norm Form Equations and Linear Divisibility Sequences

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Elisa Bellah
University of Oregon/MPIM
Wed, 2019-05-29 16:30 - 17:30
MPIM Lecture Hall

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.

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