02786nam 2200481 450 99646639240331620230616193127.0981-16-0570-X(CKB)5590000000487580(MiAaPQ)EBC6648105(Au-PeEL)EBL6648105(PPN)269152695(EXLCZ)99559000000048758020220601d2021 uy 0engurcnu---unuuutxtrdacontentcrdamediacrrdacarrierInteger sequences divisibility, Lucas and Lehmer sequences /Masum Billal and Samin RiasatGateway East, Singapore :Springer,[2021]©20211 online resource (xiii, 168 pages) illustrations981-16-0569-6 Includes bibliographical references and index.Intro -- 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.Number theoryRecurrent sequences (Mathematics)Successions (Matemàtica)thubLlibres electrònicsthubNumber theory.Recurrent sequences (Mathematics)Successions (Matemàtica)512.72Billal Masum871672Riasat SaminMiAaPQMiAaPQMiAaPQBOOK996466392403316Integer sequences2860215UNISA