Mersenne numbers which are products of two Pell numbers

Alan, Murat; Alan, Kadriye Simsek

doi:10.1007/s40590-022-00430-x

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. Mersenne numbers have been studied in the literature and various generalizations such as Mersenne-Lucas, k-Mersenne, k-Mersenne-Lucas have been studied [1,4,6,7,17,22,[25][26][27].…”

Section: Introductionmentioning

confidence: 99%

On The Hyperbolic k-Mersenne And k-Mersenne-Lucas Octonions

UYSAL,

KUMARI,

KULOĞLU

et al. 2024

KgJMat

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In this paper, we introduce the hyperbolic k-Mersenne and k-Mersenne-Lucas octonions and investigate their algebraic properties. We give Binet’s formula and present several interrelations and some well-known identities such as Catalan identity, d’Ocagne identity, Vajda identity, generating functions, etc. of these octonions in closed form. Furthermore, we investigate the relations between hyperbolic k-Mersenne octonions and hyperbolic k-Mersenne-Lucas octonions.

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Section: Introductionmentioning

confidence: 99%

On The Hyperbolic k-Mersenne And k-Mersenne-Lucas Octonions

UYSAL,

KUMARI,

KULOĞLU

et al. 2024

KgJMat

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“…In [11], S ¸iar et al found all Fibonacci or Lucas numbers that are products of two repdigits in base b. In [12], Alan and Alan discovered the Mersenne numbers that can be written in terms of the products of two Pell numbers. In [13], Rihane and Togbé obtained terms of k-Fibonacci numbers in the arrays of the Padovan or Perrin numbers.…”

Section: Introductionmentioning

confidence: 99%

On generalized order-k modified Pell and Pell–Lucas numbers in terms of Fibonacci and Lucas numbers

Daşdemir¹

2020

NNTDM

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This contribution presents all possible solutions to the Diophantine equations F k = L m L n and L k = F m F n . To be clear, Fibonacci numbers that are the product of two arbitrary Lucas numbers and Lucas numbers that are the product of two arbitrary Fibonacci numbers are determined herein. The results under consideration are proven by using Dujella-Pethö lemma in coordination with Matveev's theorem. All common terms of the Fibonacci and Lucas numbers are determined. Further, the Lucas-square Fibonacci and Fibonacci-square Lucas numbers are given.

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Fibonacci and Lucas Numbers as Products of Their Arbitrary Terms

Daşdemir,

Emin

2024

Eskişehir Technical University Journal of Science and Technology a - Applied Sciences and Engineering

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This study presents all solutions to the Diophantine equations F_k=L_m L_n and L_k=F_m F_n. To be clear, the Fibonacci numbers that are the product of two arbitrary Lucas numbers and the Lucas numbers that are the product of two arbitrary Fibonacci numbers are determined herein. The results under consideration are proven by using the Dujella-Pethő lemma in coordination with Matveev's theorem. All common terms of the Fibonacci and Lucas numbers are determined. Further, the Lucas-square Fibonacci and Fibonacci-square Lucas numbers are given.

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Mersenne numbers which are products of two Pell numbers

Cited by 3 publications

References 20 publications

On The Hyperbolic k-Mersenne And k-Mersenne-Lucas Octonions

On The Hyperbolic k-Mersenne And k-Mersenne-Lucas Octonions

On generalized order-k modified Pell and Pell–Lucas numbers in terms of Fibonacci and Lucas numbers

Fibonacci and Lucas Numbers as Products of Their Arbitrary Terms

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