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Pell–Lucas Numbers as Sum of Same Power of Consecutive Pell Numbers
Mediterranean Journal of Mathematics, 2022Let \(P_{n}\) 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 +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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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 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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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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On Pell and Pell−Lucas Hybrid Numbers
Commentationes Mathematicae, 2019In this paper we introduce the Pell and Pell−Lucas hybrid numbers as special kinds of hybrid numbers. We describe some properties of Pell hybrid numbers and Pell−Lucas hybrid numbers among other we give the Binet formula, the character and the generating function for these numbers.
Anetta Szynal-Liana, Iwona Włoch
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Repdigits base b as products of two Pell numbers or Pell–Lucas numbers
Boletín de la Sociedad Matemática Mexicana, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fatih Erduvan, Refik Keskin, Zafer Şiar
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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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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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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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