Affiliation:
1. Department of Mathematics and Statistics, The University of Calgary, Alberta, TZN IN4, Canada
Abstract
We extend the Lucas–Lehmer theory for second-order divisibility sequences to a large class of fourth-order sequences, with appropriate laws of apparition and of repetition. Examples are provided by the numbers of perfect matchings, or of spanning trees, in families of graphs, and by the numbers of points on elliptic curves over finite fields. Whether there are fourth-order divisibility sequences not covered by our theory is an open question.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
6 articles.
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1. Divisibility Sequences and Further Generalizations;CMS/CAIMS Books in Mathematics;2023
2. Richard Kenneth Guy, 1916–2020;Bulletin of the London Mathematical Society;2022-02
3. Non-homogeneous conditional recurrences;Linear and Multilinear Algebra;2017-10-03
4. Linear divisibility sequences and Salem numbers;Publicationes Mathematicae Debrecen;2017-07-01
5. Some primality tests that eluded Lucas;Designs, Codes and Cryptography;2015-05-10