Results 51 to 60 of about 145,594 (304)
Some Polynomial Sequence Relations
Mathematics, 2019 We give some polynomial sequence relations that are generalizations of the Sury-type identities. We provide two proofs, one based on an elementary identity and the other using the method of generating functions.
Chan-Liang Chung
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Coincidences in Generalized Lucas Sequences
The Fibonacci Quarterly, 2014 For an integer $k\geq 2$, let $(L_{n}^{(k)})_{n}$ be the $k-$generalized Lucas sequence which starts with $0,\ldots,0,2,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all the integers that appear in different generalized Lucas sequences; i.e., we study the Diophantine equation $L_n^{(k)}=L_m^{(\ell)
Bravo, Eric F. +2 more
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Complete solutions of the simultaneous Pell equations $ (a^2+1)y^2-x^2 = y^2-bz^2 = 1 $
AIMS Mathematics, 2021 In this paper, we consider the simultaneous Pell equations $ (a^2+1)y^2-x^2 = y^2-bz^2 = 1 $ where $ a > 0 $ is an integer and $ b > 1 $ is squarefree and has at most three prime divisors.
Changsheng Luo, Jiagui Luo
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On harmonic numbers and Lucas sequences [PDF]
Publicationes Mathematicae Debrecen, 2012 Harmonic numbers $H_k=\sum_{05 we have $$\sum_{k=0}^{p-1}u_{k+ }H_k/2^k=0 (mod p),$$ where $ =0$ if p=1,2,4,8 (mod 15), and $ =1$ otherwise.
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On the discriminator of Lucas sequences. II
, 2023 25 pages, 7 ...
Ferrari, ., Luca, F., Moree, P.
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On New Polynomial Sequences Constructed to Each Vertex in an n-Gon
Discrete Dynamics in Nature and Society, 2022 In this work, we bring to light the properties of newly formed polynomial sequences at each vertex of Pell polynomial sequences placed clockwise at each vertex in the n-gon. We compute the relation among the polynomials with such vertices.
Abdul Hamid Ganie +3 more
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Complete solutions of the simultaneous Pell's equations $ (a^2+2)x^2-y^2 = 2 $ and $ x^2-bz^2 = 1 $
AIMS Mathematics, 2023 In this paper, we consider the simultaneous Pell equations $ (a^2+2)x^2-y^2 = 2 $ and $ x^2-bz^2 = 1 $ where $ a $ is a positive integer and $ b > 1 $ is squarefree and has at most three prime divisors.
Cencen Dou, Jiagui Luo
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Brain and Behavior, Volume 12, Issue 12, December 2022., 2022 Abstract Introduction Features of underlying autonomic dysfunction, including sleep disturbances, gastrointestinal problems, and atypical heart rate, have been reported in neurodevelopmental conditions, including autism spectrum disorder (ASD). The current cross‐sectional, between‐groups study aimed to quantify symptoms of autonomic dysfunction in a ...
Antoinette S DiCriscio +6 more
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Magic numbers in the music of Sofia Gubaidulina [PDF]
Muzikologija, 2002 Sofia Gubaidulina's compositions are characterized by a special kind of symbolism and constructivism both based on numbers, i.e. mathematical proportions. In almost all her works so-called numerical plots can be detected. The proportions of the Fibonacci
Tsenova Valeria
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On the Hyperbolic Leonardo and Hyperbolic Francois Quaternions
Journal of New Theory, 2023 In this paper, we present a new definition, referred to as the Francois sequence, related to the Lucas-like form of the Leonardo sequence. We also introduce the hyperbolic Leonardo and hyperbolic Francois quaternions.
Paula Maria Machado Cruz Catarino +2 more
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