Results 31 to 40 of about 1,544,471 (165)
Solutions of the Diophantine Equations Br = Js + Jt and Cr = Js + Jt
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 Let Brr≥0, Jrr≥0, and Crr≥0 be the balancing, Jacobsthal, and Lucas balancing numbers, respectively. In this paper, the diophantine equations Br = Js + Jt and Cr = Js + Jt are completely solved. The solutions rely basically on Matveev’s theorem on linear forms in logarithms of algebraic numbers and a procedure of reducing the upper bound due to Dujella
Ahmed Gaber +2 more
wiley +1 more source
Coprime mappings and lonely runners
Mathematika, Volume 68, Issue 3, Page 784-804, July 2022., 2022 Abstract For x real, let {x}$ \lbrace x \rbrace$ be the fractional part of x (that is, {x}=x−⌊x⌋$\lbrace x\rbrace = x - \lfloor x \rfloor$). The lonely runner conjecture can be stated as follows: for any n positive integers v1
Tom Bohman, Fei Peng
wiley +1 more source
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 We use a new method of matrix decomposition for r‐circulant matrix to get the determinants of An = Circr(F1, F2, …, Fn) and Bn = Circr(L1, L2, …, Ln), where Fn is the Fibonacci numbers and Ln is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived.
Jiangming Ma +3 more
wiley +1 more source
Catalan Transform of k‐Balancing Sequences
International Journal of Mathematics and Mathematical Sciences, Volume 2021, Issue 1, 2021., 2021 In this work, the Catalan transformation (CT) of k‐balancing sequences, Bk,nn≥0, is introduced. Furthermore, the obtained Catalan transformation CBk,nn≥0 was shown as the product of lower triangular matrices called Catalan matrices and the matrix of k‐balancing sequences, Bk,nn≥0, which is an n × 1 matrix.
Asim Patra +2 more
wiley +1 more source
Binomial transform of the generalized third-order Jacobsthal sequence
, 2022 In this study, we establish the binomial transform of the generalized third-order Jacobsthal sequence. We also describe the binomial transform of four special cases of third-order Jacobsthal sequence such as the binomial transform of the third-order ...
Göcen, Melih +2 more
core +1 more source
Identities relating six members of the Fibonacci family of sequences
Karpatsʹkì Matematičnì Publìkacìï, 2022 In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences.
R. Frontczak, T. Goy, M. Shattuck
doaj +1 more source
On fourth-order jacobsthal quaternions
Journal of Mathematical Sciences and Modelling, 2018 In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions. In particular, we are interested in the generating function, Binet formula,
Gamaliel Cerda-morales
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Some Derived Sequences of K-Jacobsthal and K-Jacobsthal Lucas
International Journal of Engineering and Advanced Technology, 2019 In this article we present incredible associated some derived sequences of – Jacobsthal and – Jacobsthal Lucas numbers and we give Diophantine triples for with the ...
T. Ragunathan, G. Srividhya
openaire +1 more source
On characteristic polynomial of higher order generalized Jacobsthal numbers
Advances in Difference Equations, 2019 In this paper, we study a higher order generalization of the Jacobsthal sequence, namely, the (k,c) $(k,c)$-Jacobsthal sequence (Jn(k,c)) $(J^{(k,c)}_{n})$ for any integers n, k≥2 $k\geq 2$ and a real number c>0 $c>0$.
Diego Marques, Pavel Trojovský
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