• Title/Summary/Keyword: Lucas numbers

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NEW THEOREM ON SYMMETRIC FUNCTIONS AND THEIR APPLICATIONS ON SOME (p, q)-NUMBERS

  • SABA, N.;BOUSSAYOUD, A.
    • Journal of applied mathematics & informatics
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    • v.40 no.1_2
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    • pp.243-257
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    • 2022
  • In this paper, we present and prove an new theorem on symmetric functions. By using this theorem, we derive some new generating functions of the products of (p, q)-Fibonacci numbers, (p, q)-Lucas numbers, (p, q)-Pell numbers, (p, q)-Pell Lucas numbers, (p, q)-Jacobsthal numbers and (p, q)-Jacobsthal Lucas numbers with Chebyshev polynomials of the first kind.

Lucas-Euler Relations Using Balancing and Lucas-Balancing Polynomials

  • Frontczak, Robert;Goy, Taras
    • Kyungpook Mathematical Journal
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    • v.61 no.3
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    • pp.473-486
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    • 2021
  • We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions. From these polynomial relations, we deduce interesting identities with Fibonacci and Lucas numbers, and Euler numbers. The results must be regarded as companion results to some Fibonacci-Bernoulli identities, which we derived in our previous paper.

REPDIGITS AS DIFFERENCE OF TWO PELL OR PELL-LUCAS NUMBERS

  • Fatih Erduvan;Refik Keskin
    • Korean Journal of Mathematics
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    • v.31 no.1
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    • pp.63-73
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    • 2023
  • In this paper, we determine all repdigits, which are difference of two Pell and Pell-Lucas numbers. It is shown that the largest repdigit which is difference of two Pell numbers is 99 = 169 - 70 = P7 - P6 and the largest repdigit which is difference of two Pell-Lucas numbers is 444 = 478 - 34 = Q7 - Q4.

SUM FORMULAE OF GENERALIZED FIBONACCI AND LUCAS NUMBERS

  • Cerin, Zvonko;Bitim, Bahar Demirturk;Keskin, Refik
    • Honam Mathematical Journal
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    • v.40 no.1
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    • pp.199-210
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    • 2018
  • In this paper we obtain some formulae for several sums of generalized Fibonacci numbers $U_n$ and generalized Lucas numbers $V_n$ and their dual forms $G_n$ and $H_n$ by using extensions of an interesting identity by A. R. Amini for Fibonacci numbers to these four kinds of generalizations and their first and second derivatives.

Generalized k-Balancing and k-Lucas Balancing Numbers and Associated Polynomials

  • Kalika Prasad;Munesh Kumari;Jagmohan Tanti
    • Kyungpook Mathematical Journal
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    • v.63 no.4
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    • pp.539-550
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    • 2023
  • In this paper, we define the generalized k-balancing numbers {B(k)n} and k-Lucas balancing numbers {C(k)n} and associated polynomials, where n is of the form sk+r, 0 ≤ r < k. We give several formulas for these new sequences in terms of classic balancing and Lucas balancing numbers and study their properties. Moreover, we give a Binet style formula, Cassini's identity, and binomial sums of these sequences.

GENERALIZING SOME FIBONACCI-LUCAS RELATIONS

  • Junghyun Hong;Jongmin Lee;Ho Park
    • Communications of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.89-96
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    • 2023
  • Edgar obtained an identity between Fibonacci and Lucas numbers which generalizes previous identities of Benjamin-Quinn and Marques. Recently, Dafnis provided an identity similar to Edgar's. In the present article we give some generalizations of Edgar's and Dafnis's identities.

AREAS OF POLYGONS WITH VERTICES FROM LUCAS SEQUENCES ON A PLANE

  • SeokJun Hong;SiHyun Moon;Ho Park;SeoYeon Park;SoYoung Seo
    • Communications of the Korean Mathematical Society
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    • v.38 no.3
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    • pp.695-704
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    • 2023
  • Area problems for triangles and polygons whose vertices have Fibonacci numbers on a plane were presented by A. Shriki, O. Liba, and S. Edwards et al. In 2017, V. P. Johnson and C. K. Cook addressed problems of the areas of triangles and polygons whose vertices have various sequences. This paper examines the conditions of triangles and polygons whose vertices have Lucas sequences and presents a formula for their areas.

ON CHARACTERIZATIONS OF SOME LINEAR COMBINATIONS INVOLVING THE MATRICES Q AND R

  • Ozdemir, Halim;Karakaya, Sinan;Petik, Tugba
    • Honam Mathematical Journal
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    • v.42 no.2
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    • pp.235-249
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    • 2020
  • Let Q and R be the well-known matrices associated with Fibonacci and Lucas numbers, and k, m, and n be any integers. It is mainly established all solutions of the matrix equations c1Qn + c2Qm = Qk, c1Qn + c2Qm = RQk, and c1Qn + c2RQm = Qk with unknowns c1, c2 ∈ ℂ*. Moreover, using the obtained results, it is presented many identities, some of them are available in the literature, and the others are new, related to the Fibonacci and Lucas numbers.