Lucas Sequences

Dr. Hugh Williams is internationally recognized as an expert in computational number theory and its applications to cryptography.  He has authored over 150 refereed journal papers, 30 refereed conference papers and 20 books or book chapters.  After a university career of 46 years, he was appointed Professor Emeritus in Mathematics and Statistics at the University of Calgary.Dr. Christian Ballot was first trained as an engineer in France before studying mathematics in the US with a PhD thesis in Number Theory. He is currently Maître de Conférences at the University of Caen, Normandy. He has published about 700 pages of research papers in Arithmetic which include two memoirs of about 100 pages each.

• 1. Introduction.- 2. Basic theory of Lucas sequences.- 3. Applications.- 4. Further Properties.- 5. Some Properties of Lucasnomials.- 6. Cubic Extensions of the Lucas Sequences.- 7. Linear Recurrence Sequences and Further Generalizations.- 8. Divisibility Sequences and Further Generalizations.- 9. Prime Density of Companion Lucas Sequences.- 10. Epilogue and Open Problems.

“In this book, not only Lucas Ln sequences have been analyzed but also it is discussed that Lucas Ln sequences have found an application in dynamical systems as well as other good applications. … In the Appendix, the authors provide a short biography of Lucas’ life, where they mention some of his personality traits and discuss his legacy.” (Uğur Duran, zbMATH 1541.11001, 2024)