“…Theorem 2.5 [8] Let 𝐹 𝑛 and 𝐿 𝑛 be the 𝑛 𝑡ℎ Fibonacci number and the 𝑛 𝑡ℎ Lucas number, respectively. So, we have the following matrix equation as…”
Section: Matrices With Integer Sequencesmentioning
confidence: 99%
“…The authors have investigated applications of Fibonacci, Lucas, Pell and Pell-Lucas sequences by using matrices in [1][2][3][4]. The authors examine the relation between the suborbital graphs and Fibonacci numbers [5,6]. Then, the author finds new matrices and identities related to Fibonacci and Lucas numbers [7].…”
Section: Introductionmentioning
confidence: 99%
“…Then, the author finds new matrices and identities related to Fibonacci and Lucas numbers [7]. The relation between Pell and Pell-Lucas numbers and the suborbital graphs has been investigated in [8]. As a result, the authors produce new matrices related to these integer sequences.…”
In this paper, the matrices related to Fibonacci, Lucas, Pell, and Pell-Lucas numbers have been examined. By using these matrices new identities related to these integer sequences have been investigated.
“…Theorem 2.5 [8] Let 𝐹 𝑛 and 𝐿 𝑛 be the 𝑛 𝑡ℎ Fibonacci number and the 𝑛 𝑡ℎ Lucas number, respectively. So, we have the following matrix equation as…”
Section: Matrices With Integer Sequencesmentioning
confidence: 99%
“…The authors have investigated applications of Fibonacci, Lucas, Pell and Pell-Lucas sequences by using matrices in [1][2][3][4]. The authors examine the relation between the suborbital graphs and Fibonacci numbers [5,6]. Then, the author finds new matrices and identities related to Fibonacci and Lucas numbers [7].…”
Section: Introductionmentioning
confidence: 99%
“…Then, the author finds new matrices and identities related to Fibonacci and Lucas numbers [7]. The relation between Pell and Pell-Lucas numbers and the suborbital graphs has been investigated in [8]. As a result, the authors produce new matrices related to these integer sequences.…”
In this paper, the matrices related to Fibonacci, Lucas, Pell, and Pell-Lucas numbers have been examined. By using these matrices new identities related to these integer sequences have been investigated.
“…Recently some new studies are directly related to well known number sequences such as Fibonacci numbers, Lucas numbers, Pascal numbers, e.t.c. [13,11]. In the study [11], it is given some relationships about the Pascal and Fibonacci numbers.…”
In this study we investigate a special subgroup of the modular group
that act on the extended rationals for the aim of investigate to derived
suborbital graph. By considering this graph we give some new results
related to integer solutions to the Pell’s equation of the form x 2 − p
y 2 = 1 where p is a non-square positive integer.
In this study, new matrices which produce the Pell and Pell-Lucas numbers are given. By using these matrices, new identities and relations related to the Pell and Pell-Lucas numbers are obtained.
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