Results 41 to 50 of about 903 (200)
On Recursive Hyperbolic Fibonacci Quaternions
Communications in Advanced Mathematical Sciences, 2021 Many quaternions with the coefficients selected from special integer sequences such as Fibonacci and Lucas sequences have been investigated by a great number of researchers.
Ahmet Daşdemir
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On some links between the generalised Lucas pseudoprimes of level k
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 Pseudoprimes are composite integers sharing behaviours of the prime numbers, often used in practical applications like public-key cryptography. Many pseudoprimality notions known in the literature are defined by recurrent sequences.
Andrica Dorin +2 more
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New summation identities of hyperbolic k-Fibonacci and k-Lucas quaternions [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we introduce a set of identities involving hyperbolic k-Fibonacci quaternions and k-Lucas quaternions. Moreover, we derive summation identities for hyperbolic k-Fibonacci and k-Lucas quaternions by utilizing established properties of k ...
A. D. Godase
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ON A FIBONACCI-LIKE SEQUENCE ASSOCIATED WITH K-LUCAS SEQUENCE
Acta Universitatis Apulensis, 2017 Summary: In the present article we consider a new generalization of the classical Fibonacci sequence and we call it as Fibonacci-like sequence \(V_{k,n}\) and then we study Fibonacci-like sequence \(V_{k,n}\) and \(k\)-Lucas sequence \(L_{k,n}\) side by side by introducing two special matrices for these two sequences. After that by using these matrices
Wani, A. A. +3 more
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On a Linear Diophantine Problem Involving the Fibonacci and Lucas Sequences
Integers, 2015 See the abstract in the attached pdf.
Sanjit Singh Batra +2 more
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Divisibility Properties of the Fibonacci, Lucas, and Related Sequences [PDF]
ISRN Algebra, 2014 We use matrix techniques to give simple proofs of known divisibility properties of the Fibonacci, Lucas, generalized Lucas, and Gaussian Fibonacci numbers. Our derivations use the fact that products of diagonal matrices are diagonal together with Bezout’s identity.
Thomas Jeffery, Rajesh Pereira
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Algebraic divisibility sequences over function fields [PDF]
, 2011 In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields ...
Mahe, Valery +14 more
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Melham's sums for some Lucas polynomial sequences [PDF]
Notes on Number Theory and Discrete MathematicsA Lucas polynomial sequence is a pair of generalized polynomial sequences that satisfy the Lucas recurrence relation. Special cases include Fibonacci polynomials, Lucas polynomials, and Balancing polynomials.
Chan-Liang Chung, Chunmei Zhong
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Derivative Sequences of Fibonacci and Lucas Polynomials [PDF]
, 1991 Let us consider the Fibonacci polynomials U n(x) and the Lucas polynomials V n (x) (or simply U n and Vn, if there is no danger of confusion) defined as $$ {U_n} = x{U_{n - 1}} + {U_{n - 2}}({U_0} = 0,{U_1} = 1) $$ (1.1) and $$ {V_n} = x{V_{n - 2}}({V_0} = 2,V = x) $$ (1.2) where x is an indeterminate.
Piero Filipponi, Alwyn F. Horadam
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The Fibonacci numbers of certain subgraphs of circulant graphs
AKCE International Journal of Graphs and Combinatorics, 2015 The Fibonacci number ℱ(G) of a graph G with vertex set V(G), is the total number of independent vertex sets S⊂V(G); recall that a set S⊂V(G) is said to be independent whenever for every two different vertices u,v∈S there is no edge between them.
Loiret Alejandría Dosal-Trujillo +1 more
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