Results 51 to 60 of about 98 (97)

The extensibility of the Diophantine triple {2, b, c}

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple.
Adžaga Nikola, Filipin Alan, Jurasić Ana   +2 more
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Orthogonal forms: a simple tool for proving the irartionality of $\zeta (3)$ [PDF]

, 2009
33 pages, no figures.-- MSC2000 codes: Primary 42C05, 11B37, 11J72, 11M06; Secondary 30B70, 11A55, 11J70, 33C47.Submitted to: Journal of Approximation TheoryA new proof of the irrationality of $\zeta(3)$ is given. The orthogonality relation among certain
Arvesú Carballo, Jorge, Arvesú, Jorge
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On Doubled and Quadrupled Fibonacci Type Sequences

Annales Mathematicae Silesianae
In this paper we study a family of doubled and quadrupled Fibonacci type sequences obtained by distance generalization of Fibonacci sequence. In particular we obtain doubled Fibonacci sequence, doubled and quadrupled Padovan sequence and quadrupled ...
Yilmaz Nur Şeyma, Włoch Andrzej, Özkan Engin, Strzałka Dominik   +3 more
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Curious Continued Fractions, Nonlinear Recurrences and Transcendental Numbers [PDF]

, 2015
We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also integers), appear ...
Hone, Andrew N.W.
core  

On Generalized Jacobsthal and Jacobsthal-Lucas polynomials

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
In this paper we introduce a generalized Jacobsthal and Jacobsthal-Lucas polynomials, Jh,n and jh,n, respectively, that consist on an extension of Jacobsthal's polynomials Jn(𝑥) and Jacobsthal-Lucas polynomials jn(𝑥).
Catarino Paula, Morgado Maria Luisa
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On (k1A1, k2A2, k3A3)-Edge Colourings in Graphs and Generalized Jacobsthal Numbers

Annales Mathematicae Silesianae
In this paper we introduce a new kind of generalized Jacobsthal numbers in a distance sense. We give the identities and matrix representations for them and their connections with the Fibonacci and the Pell numbers. We also describe the interpretations of
Piejko Krzysztof, Trojnar-Spelina Lucyna
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Fibonacci Sums Modulo 5

Annales Mathematicae Silesianae
We develop closed form expressions for various finite binomial Fibonacci and Lucas sums depending on the modulo 5 nature of the upper summation limit. Our expressions are inferred from some trigonometric identities.
Adegoke Kunle, Frontczak Robert, Goy Taras   +2 more
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On Mersenne Numbers and their Bihyperbolic Generalizations

Annales Mathematicae Silesianae
In this paper, we introduce Mersenne and Mersenne–Lucas bihyperbolic numbers, i.e. bihyperbolic numbers whose coefficients are consecutive Mersenne and Mersenne–Lucas numbers.
Bród Dorota, Szynal-Liana Anetta
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Fibonacci and Telephone Numbers in Extremal Trees

Discussiones Mathematicae Graph Theory, 2018
In this paper we shall show applications of the Fibonacci numbers in edge-coloured trees. In particular we determine the successive extremal graphs in the class of trees with respect to the number of (A, 2B)-edge colourings.
Bednarz Urszula, Włoch Iwona
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A Note on Generalized Hybrid Tribonacci Numbers

Discussiones Mathematicae - General Algebra and Applications, 2020
In this paper, we introduce the generalized hybrid Tribonacci numbers. These numbers can be considered as a generalization of the generalized complex Tribonacci, generalized hyperbolic Tribonacci and generalized dual Tribonacci numbers.
Yaǧmur Tülay
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