An approach to Pillai's problem with the Pell sequence and the powers of 3

In this study, we define unrestricted Pell and Pell – Lucas hyper-complex numbers. We choose arbitrary Pell and Pell – Lucas numbers for the coefficients of the ordered basis 〖{e〗_0,e_1,⋯,e_(N-1)} of hyper-complex 2^N-ons where N∈{0,1,2,3,4} and call these hyper-complex numbers unrestricted Pell and Pell-Lucas 2N-ons. We give generating functions and Binet formulas for these type of hyper-complex numbers. We also obtain some generalization of well – known identities such as Catalan’s, Cassini’s and d’Ocagne’s identities.

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On Some New Generalized Gaussian Oresme Numbers

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2024

Ordu Üniversitesi Bilim Ve Teknoloji Dergisi

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In this study, we defined and examined a new generalization to a special sequence of rational numbers. We gave the similarities and relationships of these newly defined Gaussian Oresme numbers with the generalized Fibonacci numbers and Lucas numbers existing in the literature. Moreover, we have obtained some important identities provided by these numbers we have discussed. We also obtained the relationship of these numbers with Gaussian Fibonacci numbers.

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An approach to Pillai's problem with the Pell sequence and the powers of 3

Abstract: In this paper, we consider the Diophantine equation P n − 3 a = ν and find all ν having at least two representations. In the proof of the main theorem, we use a version of the Baker-Davenport reduction method.

Cited by 3 publications

References 20 publications

Repdigits as sums of three Half-companion Pell numbers

Repdigits as sums of three Half-companion Pell numbers

Unrestricted Pell and Pell – Lucas 2N-ons

On Some New Generalized Gaussian Oresme Numbers

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