LEADER 02786nam 2200481 450 001 996466392403316 005 20230616193127.0 010 $a981-16-0570-X 035 $a(CKB)5590000000487580 035 $a(MiAaPQ)EBC6648105 035 $a(Au-PeEL)EBL6648105 035 $a(PPN)269152695 035 $a(EXLCZ)995590000000487580 100 $a20220601d2021 uy 0 101 0 $aeng 135 $aurcnu---unuuu 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInteger sequences $edivisibility, Lucas and Lehmer sequences /$fMasum Billal and Samin Riasat 210 1$aGateway East, Singapore :$cSpringer,$d[2021] 210 4$dŠ2021 215 $a1 online resource (xiii, 168 pages) $cillustrations 311 1 $a981-16-0569-6 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- References -- Who This Book Is For -- Contents -- About the Authors -- 1 Preliminaries -- 1.1 Groups, Rings, Fields, and Vector Spaces -- 1.1.1 Groups -- 1.1.2 Rings and Fields -- 1.1.3 Vector Spaces -- 1.2 Matrices -- 1.3 Polynomials -- 1.4 Cyclotomic Polynomials -- References -- 2 Linear Recurrent Sequences -- 2.1 Introduction -- 2.2 Periodicity -- 2.3 Fundamental Theorems on Periodicity -- 2.4 Finding Pre-Period and Least Period -- References -- 3 Divisibility Sequences -- 3.1 Introduction -- 3.2 Characterization of Divisibility Sequences -- 3.3 Binomial Coefficients -- References -- 4 Lucas Sequences -- 4.1 Introduction -- 4.2 Divisibility of Second-Order Lucas Sequences -- 4.3 Lucas Sequence of Arbitrary Order -- References -- 5 Lehmer Sequences -- 5.1 Introduction -- 5.2 Divisibility of Lehmer Sequence -- 5.3 Periodicity of Lehmer Sequence -- 5.4 Extending Wilson's Theorem -- 5.5 LCM Sequence of Lehmer Sequences -- 5.6 Subsequence of Lehmer Sequences -- References -- 6 On Primitive Divisors -- 6.1 The History of Primitive Divisors -- 6.2 Primitive Divisors of an-bn -- 6.3 Primitive Divisors of Real Lucas Sequences -- 6.4 Primitive Divisors of Real Lehmer Sequences -- 6.5 Primitive Divisors of Complex Lehmer Sequences -- References -- 7 Exercises -- Reference -- Appendix Glossary -- References -- Index. 606 $aNumber theory 606 $aRecurrent sequences (Mathematics) 606 $aSuccessions (Matemātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aNumber theory. 615 0$aRecurrent sequences (Mathematics) 615 7$aSuccessions (Matemātica) 676 $a512.72 700 $aBillal$b Masum$0871672 702 $aRiasat$b Samin 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466392403316 996 $aInteger sequences$92860215 997 $aUNISA