Results 51 to 60 of about 1,000 (210)
Common values of two k-generalized Pell sequences [PDF]
Notes on Number Theory and Discrete MathematicsLet k≥2 and let (Pₙ⁽ᵏ⁾)ₙ≥₂₋ₖ be the k-generalized Pell sequence defined by Pₙ⁽ᵏ⁾=2Pₙ₋₁⁽ᵏ⁾+2Pₙ₋₂⁽ᵏ⁾+...+2Pₙ₋ₖ⁽ᵏ⁾ for n≥2 with initial conditions P₋₍ₖ₋₂₎⁽ᵏ⁾=P₋₍ₖ₋₃₎⁽ᵏ⁾=...=P₋₁⁽ᵏ⁾=P₀⁽ᵏ⁾=0, and P₁⁽ᵏ⁾=1.
Zafer Şiar +2 more
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International Journal for Research in Applied Science and Engineering Technology, 2019 The binary quadratic Diophantine equation represented by the positive pellian is analyzed for its non-zero distinct solutions. A few interesting relations among the solutions are given. Further, employing the solutions of the above hyperbola, we have obtained solutions of other choices of hyperbolas, parabolas and Pythagorean triangle.
openaire +2 more sources
Exploring the impacts of instructional modality in introductory statistics
Teaching Statistics, EarlyView.Abstract The academic experiences at colleges and universities were significantly disrupted by the coronavirus disease 2019 pandemic with notable impacts on student learning, engagement, and success. We explore its effect on academic performance and student interaction at a mid‐sized public institution in the southeastern United States.
Lindsey Bell +3 more
wiley +1 more source
Pell and Pell–Lucas Sequences of Fractional Order
Fractal and FractionalThe purpose of this paper is to introduce the fractional Pell numbers, together with several properties, via a Grünwald–Letnikov fractional operator of orders q∈(0,1) and q∈(1,2).
Jagan Mohan Jonnalagadda +1 more
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The cubic Pell equation $L$-function
Acta Arithmetica, 2023 For $d > 1$ a cubefree rational integer, we define an $L$-function (denoted $L_d(s)$) whose coefficients are derived from the cubic theta function for $\mathbb Q\left(\sqrt{-3}\right)$. The Dirichlet series defining $L_d(s)$ converges for $\text{Re}(s) > 1$, and its coefficients vanish except at values corresponding to integral solutions of $mx^3
Goldfeld, Dorian, Hinkle, Gerhardt
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British Journal of Special Education, EarlyView.Abstract As the numbers of autistic children attending school in Ireland increases, there is a growing reliance on specialised provision. Individual Education Plans (IEPs) are considered fundamental to this type of educational provision. However, emerging evidence from the Irish context reveals substantial shortcomings in the IEP process. Of particular
Laura Gormley +2 more
wiley +1 more source
On The Negative Pell Equation [PDF]
, 2017 The negative pell equation represented by the binary quadratic equationnbspnbsp is analyzed for its non-zero distinct integer solutions. A few interesting relations among the solutions are presented.
Gopalan, M. A. (M) +2 more
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Generating pairing-friendly elliptic curve parameters using sparse families
Journal of Mathematical Cryptology, 2018 The majority of methods for constructing pairing-friendly elliptic curves are based on representing the curve parameters as polynomial families. There are three such types, namely complete, complete with variable discriminant and sparse families. In this
Fotiadis Georgios, Konstantinou Elisavet
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Agroecology and Transformative Adaptation to Climate Change
Asia Pacific Viewpoint, EarlyView.ABSTRACT This paper examines transformative adaptation to climate change through the EFICAS Project (Eco‐Friendly Intensification and Climate‐resilient Agricultural Systems) implemented across 12 upland communities in northern Laos from 2014 to 2020.
Jean‐Christophe Castella
wiley +1 more source
Pell Equation. III. Graph-theoretical meaning of the solutions of the Pell equation through topological index Z [PDF]
, 2007 For a non-directed graph G composed of vertices and edges the topological index Z_G has been defined by the present author as the total sum of perfect and imperfect matchings. The Z_G values of several typical series of graphs have been known to be equal
Hosoya, Haruo, ホソヤ, ハルオ
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