Results 51 to 60 of about 237,797 (205)
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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A lucas based cryptosystem analog to the ElGamal cryptosystem and elliptic curve cryptosystem [PDF]
, 2014 In this paper, a new cryptosystem will be developed which is analogue to ElGamal encryption scheme and based on Lucas sequence in the elliptic curve group over finite field. In this encryption scheme, an Elliptic curve Diffie-Hellman (ECDH) key agreement
Koo, Lee Feng +3 more
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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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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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The Square Terms in Lucas Sequences
Journal of Number Theory, 1996 AbstractLet {Un(P, Q)} and {Vn(P, Q)} denote the Lucas sequence and companion Lucas sequence, respectively, with parametersPandQ. For all odd relatively prime values ofPandQsuch thatD=P2−4Qis positive, we determine all indicesnsuch thatUn(P, Q), 2Un(P, Q),Vn(P, Q) or 2Vn(P, Q) is a square.
Paulo Ribenboim +3 more
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On the Lucas property of linear recurrent sequences [PDF]
International Journal of Number Theory, 2016 Let [Formula: see text] be an arithmetic function. [Formula: see text] has Lucas property if for any prime [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] In this paper, we discuss the Lucas property of Fibonacci sequences and Lucas numbers. Meanwhile, we find some other interesting results.
Tianxin Cai, Hao Zhong
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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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Lucas sequence, its properties and generalisation [PDF]
, 2013 Fibonacci AND Lucas sequences are most interesting among recurrent sequences.
Barik, Biswajit
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