On Pell and Pell-Lucas Generalized Octonions
نویسندگان
چکیده
In this study, we gave a generalization on Pell and Pell-Lucas octonions over the algebra $\mathbb{O}(a,b,c)$ where $a,b$ $c$ are real numbers. For these number sequences, obtain Binet formulas some well-known identities such as Catalan's identity, Cassini's identity d'Ocagne's identity.
منابع مشابه
On Pell, Pell-Lucas, and balancing numbers
In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers. Moreover, we obtain the set of positive integer solutions of some specific Pell equations in terms of the integer sequences mentioned in the text.
متن کاملThe sum and product of Fibonacci numbers and Lucas numbers, Pell numbers and Pell-Lucas numbers representation by matrix method
Denote by {Fn} and {Ln} the Fibonacci numbers and Lucas numbers, respectively. Let Fn = Fn × Ln and Ln = Fn + Ln. Denote by {Pn} and {Qn} the Pell numbers and Pell-Lucas numbers, respectively. Let Pn = Pn × Qn and Qn = Pn + Qn. In this paper, we give some determinants and permanent representations of Pn, Qn, Fn and Ln. Also, complex factorization formulas for those numbers are presented. Key–Wo...
متن کاملk-Pell, k-Pell-Lucas and Modified k-Pell Numbers: Some Identities and Norms of Hankel Matrices
In this paper we present some identities involving terms of k-Pell, k-Pell-Lucas and Modified k-Pell sequences. We also give some results on the column and row norms of Hankel matrices which entries are numbers of these sequences. Mathematics Subject Classification: 11B37, 11B83, 15A60
متن کاملOn the intersections of Fibonacci, Pell, and Lucas numbers
We describe how to compute the intersection of two Lucas sequences of the forms {Un(P,±1)}n=0 or {Vn(P,±1)} ∞ n=0 with P ∈ Z that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers. We prove that such an intersection is finite except for the case Un(1,−1) and Un(3, 1) and the case of two V-sequences when the product of their discriminants is a perfect square. Moreover, the int...
متن کاملA Note Involving Two-by-Two Matrices of the k-Pell and k-Pell-Lucas Sequences
We use a diagonal matrix for getting the Binet’s formula for k-Pell sequence Also the n power of the generating matrix for k-Pell-Lucas sequence is established and basic properties involving the determinant allow us to obtain its Cassini’s identity. Mathematics Subject Classification: 11B37, 05A15, 11B83.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Turkish journal of mathematics & computer science
سال: 2021
ISSN: ['2148-1830']
DOI: https://doi.org/10.47000/tjmcs.780474