# Matrix divisibility sequences

@article{Cornelissen2011MatrixDS, title={Matrix divisibility sequences}, author={G. Cornelissen and J. Reynolds}, journal={arXiv: Number Theory}, year={2011} }

We show that many existing divisibility sequences can be seen as sequences of determinants of matrix divisibility sequences, which arise naturally as Jacobian matrices associated to groups of maps on affine spaces.

#### 5 Citations

New examples of determinant divisibility sequences

- Mathematics
- 2015

In this paper we consider divisibility sequences obtained from square matrices. We work with of matrix divisibility sequences associated to a semigroup and arising from endomorphisms of an affine… Expand

New Examples of Divisibility Sequences

- Mathematics, Computer Science
- Integers
- 2016

We show that if a full group of invertible matrices is embedded in an a ne space, then the determinant divisibility sequence associated with the set of endomorphisms given by taking nth powers of… Expand

Linear divisibility sequences and Salem numbers

- Mathematics
- 2017

We study linear divisibility sequences of order 4, providing a characterization by means of their characteristic polynomials and finding their factorization as a product of linear divisibility… Expand

Periodicity of the Greatest Common Divisors within Generalized Divisibility Sequences

- Mathematics
- 2019

This paper addresses divisibility properties of some families of sequences arising from partial sums of a strong divisibility sequence. In particular, we demonstrate periodicity of greatest common… Expand

Primitive divisors of sequences associated to elliptic curves over function fields

- Mathematics
- 2021

We study the existence of a Zsigmondy bound for a sequence of divisors associated to points on an elliptic curve over a function field. More precisely, let k be an algebraically closed field, let C… Expand

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