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Relevant bibliographies by topics / Pell Equation

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Academic literature on the topic 'Pell Equation'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Pell Equation"

1

Priono, Utami, Wahidah Sanusi, and Muhammad Abdy. "Aplikasi Ring Kuadratik dalam Menyelesaikan Persamaan Pell." Journal of Mathematics, Computations, and Statistics 2, no. 2 (2020): 141. http://dx.doi.org/10.35580/jmathcos.v2i2.12576.

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Artikel ini membahas tentang penerapan Metode ring (kuadratik) dalam mencari solusi pada persamaan Pell. Persamaan Pell merupakan bagian dari persamaan Diophantine non linear yang penyelesaiannya berupa bilangan bulat dengan bentuk umum persamaannya yaitu . Dalam penelitian ini persamaan Pell yang akan ditentukan solusinya yaitu . Metode yang digunakan dalam penelitian ini yaitu metode ring kuadratik. Metode ring kuadratik yang digunakan dalam menyelesaikan persamaan Pell memperhatikan konsep norm dan unit pada bilangan . Berdasarkan hasil penelitian, persamaan Pell positif memiliki paling tid

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Beck, József. "Pell equation and randomness." Periodica Mathematica Hungarica 70, no. 1 (2015): 1–108. http://dx.doi.org/10.1007/s10998-014-0064-x.

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Dubickas, Art?ras, and J�rn Steuding. "The polynomial Pell equation." Elemente der Mathematik 59, no. 4 (2004): 133–43. http://dx.doi.org/10.1007/s00017-004-0214-7.

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Sriram, S., та P. Veeramallan. "On the Integer Solution of the Transcendental Equation √2𝑧−4=√𝑥+√𝐶𝑦± √𝑥−√𝐶𝑦". Indian Journal of Advanced Mathematics (IJAM) 2, № 1 (2022): 1–4. https://doi.org/10.54105/ijam.C1120.041322.

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<strong>Abstract:</strong> Let C be a positive non-square integer. In this paper, we look at the complete solutions of the Transcendental equation √𝟐𝒛−𝟒=√𝒙+√𝑪𝒚± √𝒙−√𝑪𝒚 , where 𝒙𝟐−𝑪𝒚𝟐=𝜶𝟐 or 𝟐𝟐𝒕. In addition, we find repeated relationships in the solutions to this figure.

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Fouvry, Étienne, and Jürgen Klüners. "On the negative Pell equation." Annals of Mathematics 172, no. 3 (2010): 2035–104. http://dx.doi.org/10.4007/annals.2010.172.2035.

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Meena, K. "On the Positive Pell Equation." International Journal for Research in Applied Science and Engineering Technology 7, no. 1 (2019): 240–47. http://dx.doi.org/10.22214/ijraset.2019.1041.

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Meena, K. "On the Positive Pell Equation." International Journal for Research in Applied Science and Engineering Technology 7, no. 1 (2019): 258–65. http://dx.doi.org/10.22214/ijraset.2019.1043.

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Vidhyalakhsm, S. i. "On The Negative Pell Equation." International Journal for Research in Applied Science and Engineering Technology 7, no. 3 (2019): 891–97. http://dx.doi.org/10.22214/ijraset.2019.3156.

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Kavitha, Dr A. "On the Positive Pell Equation." International Journal for Research in Applied Science and Engineering Technology 7, no. 3 (2019): 1433–40. http://dx.doi.org/10.22214/ijraset.2019.3264.

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Pandichelvi, V., P. Sivakama sundari, and M. A. Gopalan. "On the Negative Pell Equation." International Journal of Mathematics Trends and Technology 21, no. 1 (2015): 16–20. http://dx.doi.org/10.14445/22315373/ijmtt-v21p502.

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Dissertations / Theses on the topic "Pell Equation"

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Smith, Jason. "Solvability characterizations of Pell like equations." [Boise, Idaho] : Boise State University, 2009. http://scholarworks.boisestate.edu/td/55/.

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Silva, Ronaldo Pires da. "Interseção de números geométricos via equação de Pell." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/4793.

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Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2015-10-27T14:48:51Z No. of bitstreams: 2 Dissertação - Ronaldo Pires da Silva - 2015.pdf: 1653286 bytes, checksum: 63a72d8fbcc7390f80fb41dbadaaa9fe (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-27T14:53:07Z (GMT) No. of bitstreams: 2 Dissertação - Ronaldo Pires da Silva - 2015.pdf: 1653286 bytes, checksum: 63a72d8fbcc7390f80fb41dbadaaa9fe (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<

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Van, Schenk Brill Kees. "Réhabiliter la Résonance Magnétique Nucléaire comme réalisation physique pour des ordinateurs quantiques et Résoudre des équations de Pell simultanées par des techniques de calcul quantique." Phd thesis, Université de Strasbourg, 2010. http://tel.archives-ouvertes.fr/tel-00534864.

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Cette thèse contient deux parties. Je décris une approche pour construire une réalisation physique d'un ordinateur quantique par Résonance Magnétique Nucléaire (RMN). Je propose un nouveau cadre pour la RMN dans les réalisations physiques d'un ordinateur quantique. Je construis une description de la RMN à partir de la mécanique quantique avec laquelle je peux construire les opérateurs élémentaires essentiels pour le calcul quantique. Je décris les expériences pour construire ces opérateurs. Je propose un algorithme quantique en temps polynomial pour résoudre des équations de Pell simultanées c

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CAMPOS, Danilo Albuquerque de. "Algoritmos de aproximação de raízes quadradas." Universidade Federal Rural de Pernambuco, 2014. http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/6699.

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Submitted by (lucia.rodrigues@ufrpe.br) on 2017-03-28T15:03:54Z No. of bitstreams: 1 Danilo Albuquerque de Campos.pdf: 453917 bytes, checksum: 1b07ec11128857b2e96af37543e335fe (MD5)<br>Made available in DSpace on 2017-03-28T15:03:55Z (GMT). No. of bitstreams: 1 Danilo Albuquerque de Campos.pdf: 453917 bytes, checksum: 1b07ec11128857b2e96af37543e335fe (MD5) Previous issue date: 2014-08-22<br>In this work we are interested in showing three algorithms rational approximation of square roots by methods unknown or underutilized by teachers of elementary and secondary education. We begin by defin

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Beeckmans, Laurent. "Equations de Pell, sommes des carrés consécutifs et conjecture d'Erdös." Doctoral thesis, Universite Libre de Bruxelles, 1995. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212538.

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Munoz, Susana L. "A Fundamental Unit of O_K." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/133.

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In the classical case we make use of Pells equation to compute units in the ring OF. Consider the parallel to the classical case and the quadratic field extension that creates the ring OK. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units.

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Schenk, Brill Cornelis van. "Reviving Nuclear Magnetic Resonance as a viable approach for quantum computation and solving simultaneous Pell equations by quantum computational means." Strasbourg, 2010. https://publication-theses.unistra.fr/public/theses_doctorat/2010/SCHENK_BRILL_Cornelis_Van_2010.pdf.

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Cette thèse contient deux parties. Je décris une approche pour construire une réalisation physique d'un ordinateur quantique par Résonance Magnétique Nucléaire (RMN). Je propose un nouveau cadre pour la RMN dans les réalisations physiques d'un ordinateur quantique. Je construis une description de la RMN à partir de la mécanique quantique avec laquelle je peux construire les opérateurs élémentaires essentiels pour le calcul quantique. Je décris les expériences pour construire ces opérateurs. Je propose un algorithme quantique en temps polynomial pour résoudre des équations de Pell simultanées c

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Alves, Lucinda Freese. "Aplicações de equações Diofantinas e um passeio pelo último teorema de Fermat." Universidade Federal de Goiás, 2017. http://repositorio.bc.ufg.br/tede/handle/tede/8104.

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Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2018-01-15T11:36:16Z No. of bitstreams: 2 Dissertação - Lucinda Freese Alves - 2017.pdf: 5609089 bytes, checksum: 7a1e669b3bb3ff704b41db22d3e36a4f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-01-15T11:36:54Z (GMT) No. of bitstreams: 2 Dissertação - Lucinda Freese Alves - 2017.pdf: 5609089 bytes, checksum: 7a1e669b3bb3ff704b41db22d3e36a4f (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Made avail

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Formiga, Jansen Brasileiro. "Confinamento clássico e quântico de partículas induzido pela geometria." Universidade Federal da Paraíba, 2011. http://tede.biblioteca.ufpb.br:8080/handle/tede/5698.

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Made available in DSpace on 2015-05-14T12:14:00Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1354058 bytes, checksum: 2f549ef4aed5937520237cd0b6df944f (MD5) Previous issue date: 2011-08-08<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>Since many models in physics depend on the confinement of particles in certain regions of the space-time, like Rubakov and Randall-Sundrum models, we analyze the possibility of using geometrical fields to confine particles. In doing so, we exhibit some examples of the confinement of particles by using only geometrical fields such

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Rossi, Marcelo. "Modelo matemático da resposta imune à infecção pelo vírus HIV-1." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/87/87131/tde-12012009-150807/.

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Avanços recentes nos conhecimentos sobre a infecção viral e AIDS tem levado pacientes soropositivos a uma melhor qualidade de vida. A determinação de quais populações celulares ou qual mecanismo imunológico seja mais relevante para instalação da epidemia conduz a novos patamares de possibilidades de novas drogas antiretrovirais e tratamento mais eficientes. O uso de modelagem matemática, para a epidemiologia, correlaciona indivíduos (neste caso células) e doença (o vírus) através de equações diferenciais, onde se quer observar as condições necessárias para a instalação ou não da doença. Neste

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Books on the topic "Pell Equation"

1

Jacobson, Michael J., and Hugh C. Williams. Solving the Pell Equation. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-84923-2.

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C, Williams Hugh, ed. Solving the Pell equation. Springer, 2009.

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Hinkle, Gerhardt Nicholaus Farley. The cubic Pell equation L-function. [publisher not identified], 2022.

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Pell Equation. Creative Media Partners, LLC, 2022.

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Williams, Hugh, and Michael J. Jacobson Jr. Solving the Pell Equation. Springer, 2010.

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Williams, Hugh C., and Michael J. Jr Jacobson. Solving the Pell Equation. Springer, 2009.

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Williams, Hugh, and Michael Jacobson. Solving the Pell Equation. Springer, 2008.

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Series, Michigan Historical Reprint. The Pell equation, by Edward Everett Whitford. Scholarly Publishing Office, University of Michigan Library, 2005.

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Wüstholz, Gisbert, and Clemens Fuchs, eds. Arithmetic and Geometry. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691193779.001.0001.

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This book presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures—which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria—provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings heights and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach. The first course contains recent r

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Pells Equation Problem Books in Mathematics. Springer, 2011.

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Book chapters on the topic "Pell Equation"

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Koshy, Thomas. "Pell’s Equation." In Pell and Pell–Lucas Numbers with Applications. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-8489-9_2.

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Stillwell, John. "The Pell equation." In Undergraduate Texts in Mathematics. Springer New York, 2003. http://dx.doi.org/10.1007/978-0-387-21735-2_5.

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Lemmermeyer, Franz. "The Pell Equation." In Springer Undergraduate Mathematics Series. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-78652-6_7.

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Roettger, Eric L. F., and Hugh C. Williams. "The Pell Equation." In CMS/CAIMS Books in Mathematics. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-76568-1_19.

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Williams, H. C. "Solving the Pell Equation." In Number Theory for the Millennium III. A K Peters/CRC Press, 2023. http://dx.doi.org/10.1201/9780138747022-24.

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Burger, Edward. "Solving the alleged “Pell” equation." In The Student Mathematical Library. American Mathematical Society, 2000. http://dx.doi.org/10.1090/stml/008/09.

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Jacobson, Michael J., and Hugh C. Williams. "Early History of the Pell Equation." In CMS Books in Mathematics. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-84923-2_2.

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Blomer, Valentin. "A Note on the Negative Pell Equation." In From Arithmetic to Zeta-Functions. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28203-9_2.

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Stevenhagen, Peter. "A Density Conjecture for the Negative Pell Equation." In Computational Algebra and Number Theory. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-017-1108-1_13.

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Negrepontis, Stelios, Vassiliki Farmaki, and Marina Brokou. "The Pell Equation in the Pythagoreans, Theaetetus, and Hindu Mathematics." In Handbook of the History and Philosophy of Mathematical Practice. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-40846-5_72.

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Conference papers on the topic "Pell Equation"

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Sihabudin, N. A., S. H. Sapar, and M. A. M. Johari. "Simultaneous Pell equations." In ADVANCES IN INDUSTRIAL AND APPLIED MATHEMATICS: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23). Author(s), 2016. http://dx.doi.org/10.1063/1.4954602.

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Bera, Subrata, and S. Bhattacharyya. "Effect of Charge Density on Electrokinetic Ions and Fluid Flow Through Polyelectrolyte Coated Nanopore." In ASME 2017 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/fedsm2017-69194.

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We have studied the electroosmotic flow (EOF) and its effect through a polyelectrolyte coated conical nanopore. The nanopore wall bears a uniform negative surface charge while charged density of the polyelectrolyte layer (PEL) bears positive charge. The degree of softness in the PEL is mainly affects the hydrodynamic field inside the nanopore while ionic current is not affected significantly by flow field. The characteristic of electrokinetic flow is based on the nonlinear Nernst-Planck equations for the ion transport coupled with the Brinkman extended Navier-Stokes equations for fluid flow an

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Mazhari, Emad, and Sayed A. Nassar. "Modeling of Moisture Diffusion Effect on Peel and Sheer Stresses in Adhesively Bonded Single Lap Joints Under Shear-Tensile Loading." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-70127.

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In this study, the Fickian diffusion formulation is extended to the adhesive layer of a single lap joint model, in order to develop a coupled peel and shear stress-diffusion model. Constitutive equation are formulated for shear and peel stresses in terms of adhesive material properties that are time and location-dependent. Numerical solution is provided for the effect of diffusion on shear and peel stresses distribution. Detailed discussion of the results is presented.

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Mazurkin, Peter Matveevich, and Yana Oltgovna Georgieva. "WAVELET ANALYSIS OF HEIGHT AT POINTS OF THE CHANNEL OF A SMALL RIVER FROM THE MOUTH ON SPACE IMAGES." In GEOLINKS International Conference. SAIMA Consult Ltd, 2020. http://dx.doi.org/10.32008/geolinks2020/b1/v2/31.

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The purpose of the article is to analyze asymmetric wavelets of changing the coordinate - the local elevation of the Irovka river channel, as well as the influence of local latitude and longitude on it of 290 characteristic points along the river channel from source to mouth. After identifying the general wavelet equation, 12 terms were obtained in the form of asymmetric wavelets with variable amplitude and oscillation period. The first three members gave a correlation coefficient of 0.9993, which is slightly less than for latitude 0.9999, but more than for longitude 0.9991. As a result, all t

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Niu, R. J., and P. Huang. "Numerical Analysis for Influence of Plastic and Elastic Deformation of Rough Surfaces on PEHL for Line Contacts." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80314.

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In the present paper, analysis of elasto-plasto-hydrodynamic lubrication (PEHL) in the line contact is carried out to investigate the effect of heavily loaded roll-over on the change in profile of indents. The pressure and film thickness profiles are obtained to solve the Reynolds and film thickness equations simultaneously. And, both the elastic and plastic deformations of the contact, featured with an indent, have been considered. A multi-grid numerical algorithm used in EHL of line contacts is modified and then used for the oil lubricated rolling contacts. In the program, stress and plastic

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Gerini-Romagnoli, Marco, and Sayed A. Nassar. "2-D Analytical Model of Heat and Moisture Diffusion in Bonded Single Lap Joints." In ASME 2022 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/imece2022-95201.

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Abstract A two-dimensional elastic analytical model for bonded single lap joints subjected to heat and moisture diffusion is presented. The distributions of peel and shear stress in the bond area are calculated. Local moisture concentration and bondline temperature determine the properties of the adhesive layer, which vary in the space and time coordinates. Adhesive diffusivity coefficient and absolute saturated concentration are affected by the material temperature, and scenarios of individual and combined heat and moisture diffusion are analyzed. The governing partial differential equations

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Shahin, Khaled, and Farid Taheri. "A Simple and Practical Solution for Characterization of Adhesively Bonded Joints in Dissimilar Materials." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-44115.

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Fiber-reinforced polymer (FRP) composites are increasingly used in structural systems, replacing structural steel and aluminum. It is now well established that adhesive bonding is the most efficient mean of joining composites. Unfortunately, analytical models available in the literature offer design equations mainly applicable to balanced adhesive joints; where the two adherends are identical. In many practical applications, however, FRP composites are used (joined) in conjunction with other materials. This paper presents a simplified model that accurately predicts the behaviour of adhesive jo

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Gray, Donald G. "A Process and Economic Model for the Real-Time Optimization of Operating Profit in a Citrus Feedmill." In ASME 2007 Citrus Engineering Conference. American Society of Mechanical Engineers, 2007. http://dx.doi.org/10.1115/cec2007-5303.

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During the past 6 years, increases in energy costs have adversely impacted the profitability of feedmill operations. The market values of dried feed, molasses, and d-limonene have not sufficiently increased to offset this additional cost. Lacking alternatives to processing wet peel, many of the large citrus processors have operated feedmills at a financial loss. The optimal operation of a citrus feedmill requires that a combination of process, resource cost, and product market value data be analyzed and translated into actions that will maximize operating profit or minimize operational losses.

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Tang, Dan X., Bruno Barthelemy, and Heng Yuan. "Self-Pierced Rivet (SPR) Modeling in Aluminum Structure Crash Analysis." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-39078.

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A finite element method has been developed for modeling the characteristics of self-pierced rivets (SPR) in the aluminum parts and structures subjected to impact. It considers SPR elastic, inelastic and separation behaviors and was developed based on the coupon test results in lap shear, coach peel, and tension modes. The method consists of establishing baseline strength characteristics in the six degrees of freedom; and then modifying the baseline properties with coefficient factors (Ki) factors that influence the performance of SPR (thickness, differences in material, temperature, impact vel

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