Results 61 to 70 of about 209 (127)
Annales Mathematicae SilesianaeWe 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 +2 more
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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 parametric family of quartic Thue inequalities
, 2011 Secondary: 11A07, 11B37, 11D75, 11J68, 11J70 ...
Husna Zayadi
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On Mersenne Numbers and their Bihyperbolic Generalizations
Annales Mathematicae SilesianaeIn 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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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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A new member of the Pell sequences: The pseudo-Pell sequence
In this study, we define a new family of the Pell numbers and establish some properties of the relation to the ordinary Pell numbers. We give some identities the pseudo-Pell numbers.
GÖKBAŞ, Hasan
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On a New One Parameter Generalization of Pell Numbers
Annales Mathematicae Silesianae, 2019 In this paper we present a new one parameter generalization of the classical Pell numbers. We investigate the generalized Binet’s formula, the generating function and some identities for r-Pell numbers.
Bród Dorota
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, 2020 In this paper we find closed forms for certain finite sums. In each case the denominator of the summand consists of products of generalized Fibonacci numbers.
R S Melham
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A note on some Diophantine equations
, 2017 Let k 3 be an odd integer. In this paper we investigate all positive integer solutions of the equations x4 kx2yCy2D A, x4 kx2yCy2D A.k2 4/; x4 .k2 4/y2D 4A; and x2 .k2 4/y4 D 4A with AD .k 2/: We show that if k 1.mod8/ and k2 4 be a square-free integer ...
Refik Keskin, M. Duman
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On Diophantine equations involving Lucas sequences
Open Mathematics, 2019 In this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequence and R, P and Q are polynomials (under weak assumptions).
Trojovský Pavel
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