LEADER 03764nam 22004815 450 001 9910754099203321 005 20231019183345.0 010 $a3-031-37238-7 024 7 $a10.1007/978-3-031-37238-4 035 $a(MiAaPQ)EBC30799973 035 $a(Au-PeEL)EBL30799973 035 $a(DE-He213)978-3-031-37238-4 035 $a(PPN)272917664 035 $a(EXLCZ)9928528636500041 100 $a20231019d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Lucas Sequences$b[electronic resource] $eTheory and Applications /$fby Christian J.-C. Ballot, Hugh C. Williams 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (312 pages) 225 1 $aCMS/CAIMS Books in Mathematics,$x2730-6518 ;$v8 311 08$aPrint version: Ballot, Christian J. -C. The Lucas Sequences Cham : Springer International Publishing AG,c2023 9783031372377 327 $a1. 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. . 330 $aAlthough the Lucas sequences were known to earlier investigators such as Lagrange, Legendre and Genocchi, it is because of the enormous number and variety of results involving them, revealed by Édouard Lucas between 1876 and 1880, that they are now named after him. Since Lucas? early work, much more has been discovered concerning these remarkable mathematical objects, and the objective of this book is to provide a much more thorough discussion of them than is available in existing monographs. In order to do this a large variety of results, currently scattered throughout the literature, are brought together. Various sections are devoted to the intrinsic arithmetic properties of these sequences, primality testing, the Lucasnomials, some associated density problems and Lucas? problem of finding a suitable generalization of them. Furthermore, their application, not only to primality testing, but also to integer factoring, efficient solution of quadratic and cubic congruences, cryptography and Diophantine equations are briefly discussed. Also, many historical remarks are sprinkled throughout the book, and a biography of Lucas is included as an appendix. Much of the book is not intended to be overly detailed. Rather, the objective is to provide a good, elementary and clear explanation of the subject matter without too much ancillary material. Most chapters, with the exception of the second and the fourth, will address a particular theme, provide enough information for the reader to get a feel for the subject and supply references to more comprehensive results. Most of this work should be accessible to anyone with a basic knowledge of elementary number theory and abstract algebra. The book?s intended audience is number theorists, both professional and amateur, students and enthusiasts. 410 0$aCMS/CAIMS Books in Mathematics,$x2730-6518 ;$v8 606 $aNumber theory 606 $aNumber Theory 615 0$aNumber theory. 615 14$aNumber Theory. 676 $a512.72 700 $aBallot$b Christian J. -C$01433969 701 $aWilliams$b Hugh C$0309295 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910754099203321 996 $aThe Lucas Sequences$93585040 997 $aUNINA