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Pell and Pell-Lucas numbers as sums of two Jacobsthal numbers
, 2022 First ...
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Pell and Pell-Lucas numbers as sums of three repdigits
, 2020 Same work has been study by another ...
Bhoi, Kisan +2 more
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On the Domain of the Pell-Lucas Matrix in the Spaces c and c_0
Dera Natung Government College Research JournalIn this study, we introduce new Banach sequence spaces $c(\Theta), c_0(\Theta)$, defined via a regular infinite matrix $ \Theta = (\lambda_{nk})$, where \[ \Theta_{nk} = \begin{cases} \dfrac{2\lambda_k}{3\lambda_n+\lambda_{n-1}} & 0 \leq k \leq n ...
Shiva Shah
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Deriving Binomial Convolution Formulas for Horadam Sequences via Context-Free Grammars
AxiomsThe Horadam sequence Hn(a,b;p,q) unifies a number of well-known sequences, such as Fibonacci and Lucas sequences. We use the context-free grammars as a new tool to study Horadam sequences.
Jun-Ying Liu +3 more
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A Note on Generalized k-Order F&L Hybrinomials
AxiomsIn this study, we introduce generalized k-order Fibonacci and Lucas (F&L) polynomials that allow the derivation of well-known polynomial and integer sequences such as the sequences of k-order Pell polynomials, k-order Jacobsthal polynomials and k-order ...
Süleyman Aydınyüz +1 more
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On Mixed 𝐵-Concatenations of Pell and Pell–Lucas Numbers which are Pell Numbers
Mathematica PannonicaLet (𝑃𝑛)𝑛≥0 and (𝑄𝑛)𝑛≥0 be the Pell and Pell–Lucas sequences. Let 𝑏 be a positive integer such that 𝑏 ≥ 2. In this paper, we prove that the following two Diophantine equations 𝑃𝑛 = 𝑏𝑑𝑃𝑚 + 𝑄𝑘 and 𝑃𝑛 = 𝑏𝑑𝑄𝑚 + 𝑃𝑘 with 𝑑, the number of digits of 𝑃𝑘 or 𝑄𝑘 in base 𝑏, have only finitely many solutions in nonnegative integers (𝑚, 𝑛, 𝑘, 𝑏, 𝑑).
Adédji, Kouéssi Norbert +1 more
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Some sum formulas for products of Pell and Pell-Lucas numbers [PDF]
International Journal of Advances in Applied Mathematics and Mechanics, 2017 Hasan GÖKBA ̧S, Hasan KÖSE
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On Reciprocal Sums of Products of Pell-Lucas Numbers
International Journal of Mathematical Analysis, 2019 openaire +1 more source
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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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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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