What is it about?

In this paper, for an integer which is square-free, we show that there is at most one value of the positive integer x participating in the Pell equation x^2-dy^2=+/-1, which is a k–generalized Fibonacci number, with a couple of parametric exceptions which we completely characterize.

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Why is it important?

Applies Baker's methods

Perspectives

Computations in Mathematica

Dr.rer.nat. M.Sc. Mahadi Ddamulira
Technische Universitat Graz

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This page is a summary of: On the x–coordinates of Pell equations which are k–generalized Fibonacci numbers, Journal of Number Theory, February 2020, Elsevier, DOI: 10.1016/j.jnt.2019.07.006.
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