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Pell and Pell–Lucas Numbers as Product of Two Repdigits
Mathematical Notes, 2022Let \( (P_n)_{n\ge 0} \) and \( (Q_n)_{n\ge 0} \) be the sequences of Pell and Pell-Lucas numbers, respectively, given by the linear recurrences: \( P_0=0, P_1=1 \), \( Q_0=2, Q_1=2 \), and \( P_{n+2}=2P_{n+1}+P_n \) and \( Q_{n+2}=2Q_{n+1}+Q_n \) for all \( n\ge 0 \).
Erduvan, F., Keskin, R.
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On Pell Quaternions and Pell-Lucas Quaternions [PDF]
Advances in Applied Clifford Algebras, 2016 WOS:000370339300004The main object of this paper is to present a systematic investigation of new classes of quaternion numbers associated with the familiar Pell and Pell-Lucas numbers.
Çimen, CENNET +5 more
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A Short Note on the Pell-Lucas–Eisenstein Series [PDF]
Asian-European Journal of Mathematics, 2022 In this work, we define a new type of Eisenstein-like series by using Pell-Lucas numbers and call them the Pell-Lucas-Eisenstein Series. Firstly, we show that the Pell-Lucas-Eisenstein series are convergent on their domain.
İlker İnam, Engin Özkan
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Perfect Pell and Pell–Lucas numbers
Studia Scientiarum Mathematicarum Hungarica, 2019Abstract The Pell sequence is given by the recurrence Pn = 2Pn−1 + Pn−2 with initial condition P0 = 0, P1 = 1 and its associated Pell-Lucas sequence is given by the same recurrence relation but with initial condition Q0 = 2, Q1 = 2. Here we show that 6 is the only perfect number appearing in these sequences.
Jhon J. Bravo, Florian Luca
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On the problem of Pillai with Pell numbers, Pell–Lucas numbers and powers of 3
International Journal of Number Theory, 2022Let [Formula: see text] be the sequence of Pell numbers defined by [Formula: see text], [Formula: see text] and [Formula: see text] for all [Formula: see text] and let [Formula: see text] be its companion sequence, the Pell–Lucas numbers defined by [Formula: see text] and [Formula: see text] for all [Formula: see text].
Faye, Bernadette, Edjeou, Bilizimbéyé
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Pell and Pell–Lucas Numbers as Sums of Two Repdigits
Bulletin of the Malaysian Mathematical Sciences Society, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chèfiath Adegbindin +2 more
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Some properties of starlike functions subordinate to k-Pell–Lucas numbers
Boletín de la Sociedad Matemática Mexicana, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Şahsene Altınkaya +2 more
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Pell Numbers, Pell–Lucas Numbers and Modular Group
Algebra Colloquium, 2007We show that the matrix A(g), representing the element g = ((xy)2(xy2)2)m (m ≥ 1) of the modular group PSL(2,Z) = 〈x,y : x2 = y3 = 1〉, where [Formula: see text] and [Formula: see text], is a 2 × 2 symmetric matrix whose entries are Pell numbers and whose trace is a Pell–Lucas number. If g fixes elements of [Formula: see text], where d is a square-free
Q. Mushtaq, U. Hayat
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Common Factors of Pell and Pell-Lucas numbers
2021Progress in Applied Science and Technology, 11, 1, 7 ...
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2014
Like Fibonacci and Lucas numbers, the Pell family is ubiquitous. Pell and Pell–Lucas numbers also provide boundless opportunities to experiment, explore, and conjecture; they are a lot of fun for inquisitive amateurs and professionals alike. In this chapter, we formally introduce the family, and cite their occurrences in earlier chapters, as well as ...
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Like Fibonacci and Lucas numbers, the Pell family is ubiquitous. Pell and Pell–Lucas numbers also provide boundless opportunities to experiment, explore, and conjecture; they are a lot of fun for inquisitive amateurs and professionals alike. In this chapter, we formally introduce the family, and cite their occurrences in earlier chapters, as well as ...
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