Results 181 to 190 of about 2,867 (218)

Pell and Pell–Lucas Numbers as Sums of Two Repdigits

Bulletin of the Malaysian Mathematical Sciences Society, 2019
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Alain Togbé, Florian Luca, Togbé Alain   +2 more
exaly   +3 more sources

AN INTEGRAL REPRESENTATION OF THE PELL NUMBERS AND THE PELL-LUCAS NUMBERS [PDF]

Journal of Science Natural Science
We 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. [PDF]

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 [PDF]

, 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, 2022
Let \( (P_n)_{n\ge 0} \) 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, 2023
In 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, 2022
Let [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–Lucas Numbers as Sum of Same Power of Consecutive Pell Numbers

Mediterranean Journal of Mathematics, 2022
Let \(P_{n}\) be the \(n\)-th term of the Pell sequence defined as \(P_{0}=0, P_{1}=1, P_{n}=2P_{n+1}+P_{n}\) and let \(Q_{n}\) be the \(n\)-th term of the Pell-Lucas sequence defined as \(Q_{0}=Q_{1}=2, Q_{n}=2Q_{n-1}+Q_{n-2}\). The authors are interested in non-negative integers \((m, n, k, x)\) solutions of the Diophantine equation \[ P_{n}^{x}+P_{n+
Salah Eddine Rihane, Euloge B. Tchammou, Alain Togbé   +2 more
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Perfect Pell and Pell–Lucas numbers

Studia Scientiarum Mathematicarum Hungarica, 2019
Abstract 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, 2007
We 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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