TL;DR
This paper surveys properties of divisibility sequences, focusing on the law of apparition and repetition, highlighting historical developments and the need for a comprehensive overview in this mathematical area.
Contribution
It provides a systematic survey of divisibility sequences, consolidating scattered results and emphasizing the importance of these properties in number theory.
Findings
Identifies key properties of divisibility sequences
Highlights historical rediscoveries of results
Underscores the need for a unified survey in the field
Abstract
The purpose of this memoir is to discuss two very interesting properties of integer sequences. One is the law of apparition and the other is the law of repetition. Both have been extensively studied by mathematicians such as Ward, Lucas, Lehmer, Hall, etc. However, due to the lack of a proper survey in this area, many results have been rediscovered many decades later. This along with the necessity of the usefulness of such theory calls for a survey on this topic.
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Taxonomy
TopicsCellular Automata and Applications