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AN INTEGRAL REPRESENTATION OF THE PELL NUMBERS AND THE PELL-LUCAS NUMBERS
Journal of Science Natural ScienceWe report on an integral representation for the Pell sequence, Pell-Lucas sequence, Balancing sequence and Lucas-Balancing sequence. This integral representation is based on the generating function and the Binet-like formulas of the aforementioned sequences.
null Luu Ba Thang, null Nguyen Duc Sang
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The Binet Formulas for the Pell and Pell-Lucas p-Numbers.
Ars Comb., 2007 In this paper, we define the Pell and Pell-Lucas p-numbers and derive the analytical formulas for these numbers. These formulas are similar to Bin et's formula for the classical Pell numbers.
Kocer, E. Gokcen, Tuglu, Naim
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Pell and Pell–Lucas Numbers with Applications
, 2014 Pell and Pell–Lucas Numbers has been carefully crafted as an undergraduate/graduate textbook; the level of which depends on the college/university and the instructor’s preference.
Koshy, Thomas
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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 applications of Pell and Pell-Lucas numbers with matrix method
Journal of Intelligent & Fuzzy Systems, 2023In this study, new matrices which produce the Pell and Pell-Lucas numbers are given. By using these matrices, new identities and relations related to the Pell and Pell-Lucas numbers are obtained.
Ümmügülsün Akbaba, Ali H. Deger
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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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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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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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The Fibonacci Quarterly, 1972
Pell numbers are generated by the sequence \(P_{n+2} = 2P_{n+1} + P_n\) \((P_0 = 0,\ P_1 = 1)\) and the solution in integers of the equation \(x^2 + y^2 = z^2\) is given by \(x = 2pq\), \(y = p^2 - q^2\). Let \(y - x = \pm c\). The author states that when \(c =1\) the values of \(p\) and \(q\) are Pell numbers and shows that when \(c \ne1\) then the ...
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Pell numbers are generated by the sequence \(P_{n+2} = 2P_{n+1} + P_n\) \((P_0 = 0,\ P_1 = 1)\) and the solution in integers of the equation \(x^2 + y^2 = z^2\) is given by \(x = 2pq\), \(y = p^2 - q^2\). Let \(y - x = \pm c\). The author states that when \(c =1\) the values of \(p\) and \(q\) are Pell numbers and shows that when \(c \ne1\) then the ...
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Generalized Identities for third order Pell Number, Pell-Lucas Number and Modified Pell Number
2020วารสารวิทยาศาสตร์และเทคโนโลยี มทร.ธัญบุรี, 10, 1, 96 ...
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