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Dissertations / Theses on the topic 'Diophantine equation'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Bartolomé, Boris. "Diophantine equations and cyclotomic fields." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0104/document.

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Cette thèse examine quelques approches aux équations diophantiennes, en particulier les connexions entre l’analyse diophantienne et la théorie des corps cyclotomiques.Tout d’abord, nous proposons une introduction très sommaire et rapide aux méthodes d’analyse diophantienne que nous avons utilisées dans notre travail de recherche. Nous rappelons la notion de hauteur et présentons le PGCD logarithmique.Ensuite, nous attaquons une conjecture, formulée par Skolem en 1937, sur une équation diophantienne exponentielle. Pour cette conjecture, soit K un corps de nombres, α1 ,…, αm , λ1 ,…, λm des élém

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2

Ren, Ai. "Embedded Surface Attack on Multivariate Public Key Cryptosystems from Diophantine Equation." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1558364211159262.

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3

Weeman, Glenn Steven. "A Diophantine Equation for the Order of Certain Finite Perfect Groups." University of Akron / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=akron1396902470.

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4

Rahimi, Shahriar. "A NOVEL LINEAR DIOPHANTINE EQUATION-BAESD LOW DIAMETER STRUCTURED PEER-TO-PEER NETWORK." OpenSIUC, 2017. https://opensiuc.lib.siu.edu/dissertations/1462.

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This research focuses on introducing a novel concept to design a scalable, hierarchical interest-based overlay Peer-to-Peer (P2P) system. We have used Linear Diophantine Equation (LDE) as the mathematical base to realize the architecture. Note that all existing structured approaches use Distributed Hash Tables (DHT) and Secure Hash Algorithm (SHA) to realize their architectures. Use of LDE in designing P2P architecture is a completely new idea; it does not exist in the literature to the best of our knowledge. We have shown how the proposed LDE-based architecture outperforms some of the most we

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5

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

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6

Синиця, О. "Методи розв'язування діофантових рівнянь". Thesis, Cумський державний університет, 2016. http://essuir.sumdu.edu.ua/handle/123456789/48885.

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Розв’язок рівнянь в цілих числах є однією з стародавніх математичних задач. Основне джерело, яке дійшло до наших часів – видання праці Діофанта «Арифметика». На жаль, з тринадцяти книг, що входили до цього видання, тільки шість збереглися до Середніх віків, саме вони і стали джерелом натхнення для багатьох математиків.

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7

Maximenko, Marianna. "Contribution au calcul de la solution générale d'équations en mots." Rouen, 1995. http://www.theses.fr/1995ROUE5003.

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Le problème central de la thèse est d'effectuer les recherches du calcul de la solution générale d'équations en mots, donnée sous la forme d'un ensemble fini de collections paramétrées de solutions. Ce projet a été proposé par G. S. Makanin. Nous avons proposé dans ce travail un algorithme quasi linéaire du calcul de la solution générale de l'équation en mots à une variable avec des coefficients. Nous avons décrit la solution générale de l'équation miroir sous la forme des mots à vecteurs. En introduisant la notion d'invariant de Makanin, nous avons obtenu la caractéristique du graphe de l'équ

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8

Валенкевич, М. Є. "Діофантові рівняння". Thesis, Сумський державний університет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/38857.

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9

Wellstead, Kevin. "Robust polynomial controller design." Thesis, Brunel University, 1991. http://bura.brunel.ac.uk/handle/2438/4866.

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The work presented in this thesis was motivated by the desire to establish an alternative approach to the design of robust polynomial controllers. The procedure of pole-placement forms the basis of the design and for polynomial systems this generally involves the solution of a diophantine equation. This equation has many possible solutions which leads directly to the idea of determining the most appropriate solution for improved performance robustness. A thorough review of many of the aspects of the diophantine equation is presented, which helps to gain an understanding of this extremely impor

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10

Опарій, О. С. "Застосування генетичного алгоритму до розв'язання діафантових рівнянь". Thesis, Сумський державний університет, 2013. http://essuir.sumdu.edu.ua/handle/123456789/40956.

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У даній роботі розглядається застосування генетичного алгоритму до розв’язання діафантового рівняння першого порядку. Генетичні алгоритми є потужним обчислювальним засобом для різних оптимізаційних задач. Ці алгоритми застосовуються у найрізноманітніших галузях: економіці, фізиці, технічних науках і т.п.

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11

Lee, Ellyn Jay. "Studies on diophantine equations." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239075.

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12

Mabaso, Automan Sibusiso. "Some exponential diophantine equations." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85587.

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Thesis (MSc)--Stellenbosch University, 2013.<br>ENGLISH ABSTRACT: The aim of this thesis is to study some methods used in solving exponential Diophan- tine equations. There is no generic method or algorithm that can be used in solving all Diophantine equations. The main focus for our study will be solving the exponential Dio- phantine equations using the modular approach and the linear forms in two logarithms approach.<br>AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om sommige metodes te bestudeer om sekere Diophantiese vergelykings op te los. Daar is geen metode wat alle Diophanti

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13

Yesilyurt, Deniz. "Solving Linear Diophantine Equations And Linear Congruential Equations." Thesis, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-19247.

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This report represents GCD, euclidean algorithm, linear diophantine equation and linear congruential equation. It investigates the methods for solving linear diophantine equations and linear congruential equations in several variables. There are many examples which illustrate the methods for solving equations.

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14

Smart, Nigel Paul. "The computer solution of diophantine equations." Thesis, University of Kent, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315089.

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15

Long, Rachel Louise. "The algorithmic solution of simultaneous diophantine equations." Thesis, Oxford Brookes University, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444340.

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16

Baczkowski, Daniel M. "Diophantine Equations Involving Arithmetic Functions of Factorials." Miami University / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=miami1088086258.

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17

Akhtari, Shabnam. "Thue equations and related topics." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/1288.

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Using a classical result of Thue, we give an upper bound for the number of solutions to a family of quartic Thue equations. We also give an upper bound upon the number of solutions to a family of quartic Thue inequalities. Using the Thue-Siegel principle and the theory of linear forms in logarithms, an upper bound is given for general quartic Thue equations. As an application of the method of Thue-Siegel, we will resolve a conjecture of Walsh to the effect that the Diophantine equation aX⁴ - bY² = 1, for fixed positive integers a and b, possesses at most two solutions in positive integers X a

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18

Schindler, Damaris. "On diophantine equations involving norm forms and bihomogeneous forms." Thesis, University of Bristol, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.601162.

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If the descent theory, developed by Colliot-Thelene and Sansuc, applies, then it can reduce the question of understanding whether the Brauer-Manin obstruction is the only one to understanding weak approximation on the resulting descent varieties. In some cases the descent varieties are easier to handle and accessible by analytic methods as for example t he circle method. In joint work with A. Skorobogatov we followed this approach focusing on varieties corresponding to the representation of a norm form by a product of linear polynomials. We present this work in the first part of this thesis wh

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19

Ibrahim, Mostafa. "Modular and reciprocity approaches to a family of diophantine equations." Thesis, University of Warwick, 2009. http://wrap.warwick.ac.uk/2761/.

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In this thesis we study the Diophantine equation xp - Dy2p = z2; gcd(x; z) = 1; p prime: We combine two approaches: - The modular approach using in Wiles's proof of Fermat's Last Theorem. - Elementary quadratic reciprocity. We show how using this combination of approaches and computer calculations we can get congruence conditions for the exponent p.

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20

蔡國光 and Kwok-kwong Stephen Choi. "Some explicit estimates on linear diophantine equations in three primevariables." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1990. http://hub.hku.hk/bib/B3120966X.

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21

Kaminski, Lance. "A discussion of homogenous quadratic equations." Thesis, Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/1630.

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22

Ma, Fei Chun. "A Diophantine equations based cipher for Internet EDI security in Macau." Thesis, University of Macau, 1997. http://umaclib3.umac.mo/record=b1445591.

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23

Choi, Kwok-kwong Stephen. "Some explicit estimates on linear diophantine equations in three prime variables /." [Hong Kong] : University of Hong Kong, 1990. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12907236.

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24

Vieira, José Carlos Chaves. "Estudo numérico das bifurcações do sistema regulador de Watt." Universidade do Estado de Santa Catarina, 2011. http://tede.udesc.br/handle/handle/2009.

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Made available in DSpace on 2016-12-12T20:15:54Z (GMT). No. of bitstreams: 1 pre_textuais.pdf: 54354 bytes, checksum: 81cdd6a9b6a26b1b93efdeee869b2de9 (MD5) Previous issue date: 2011-07-26<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>In this work we study the self-organization of periodic structures on parameter-spaces of the largest Lyapunov exponent (Lyapunov diagrams) of the Watt governor system model. A hierarchical organization and period-adding bifurcation cascades of the periodic structures are observed, and these self-organized cascades accumulate on a periodic b

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25

Beauchamp, Bradley K. McCrone Sharon Rich Beverly Susan. "Exploring calculus students' understanding of L'Hôpital's Rule." Normal, Ill. : Illinois State University, 2006. http://proquest.umi.com/pqdweb?index=0&did=1273094441&SrchMode=1&sid=3&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1181240966&clientId=43838.

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Thesis (Ph. D.)--Illinois State University, 2006.<br>Title from title page screen, viewed on June 7, 2007. Dissertation Committee: Dissertation Committee: Sharon S. McCrone, Beverly S. Rich (co-chairs), James F. Cottrill, Lucian L. Ionescu. Includes bibliographical references (leaves 155-159) and abstract. Also available in print.

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26

Haristoy, Julien. "Equations diophantiennes exponentielles." Université Louis Pasteur (Strasbourg) (1971-2008), 2003. http://www.theses.fr/2003STR13123.

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27

Nguyen, Phu Qui Pierre. "Equations de Mahler et hypertranscendance." Paris 6, 2012. http://www.theses.fr/2012PA066809.

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Soit K un corps équipé d'un endomorphisme \sigma. Dans cette thèse, nous montrons que la théorie de Galois aux \sigma-différences bien connue dans le cas où \sigma est un automorphisme du corps K peut être adaptée au cas où \sigma n'est plus nécessairement surjectif, en passant à la clôture inversive de K. Nous utilisons ensuite cette théorie de Galois pour donner un critère d'indépendance algébrique pour les solutions de \sigma-équations du premier ordre. Ce résultat nous permet de caractériser les solutions hyperalgébriques de ces \sigma-équations lorsque K est muni d'une dérivation vérifian

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28

Hanine, El Mostafa. "Equations diophantiennes p-adiques et congruences modulo p2." Toulouse 3, 1990. http://www.theses.fr/1990TOU30088.

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On demontre que pour tout entier naturel d, il existe un plus petit entier p(d) tel que si p est un nombre premier superieur ou egal a p(d) et f,z#px#1. . . , x#2#d#+#1 sans terme constant de degre d l'equation f(x#1. . . , x#2#d#+#1)0(p#2) admet une solution primitive. On demontre aussi que p(2)=2p(3)=3,p(d)>2 si d4 et p(d)>p si d est multiple de p#2p avec p=2

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29

Allen, Patrick. "Multiplicities of Linear Recurrence Sequences." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2942.

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In this report we give an overview of some of the major results concerning the multiplicities of linear recurrence sequences. We first investigate binary recurrence sequences where we exhibit a result due to Beukers and a result due to Brindza, Pintér and Schmidt. We then investigate ternary recurrences and exhibit a result due to Beukers building on work of Beukers and Tijdeman. The last two chapters deal with a very important result due to Schmidt in which we bound the zero-multiplicity of a linear recurrence sequence of order <em>t</em> by a function involving <em>t</em> alo

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30

Heimonen, A. (Ari). "On effective irrationality measures for some values of certain hypergeometric functions." Doctoral thesis, University of Oulu, 1997. http://urn.fi/urn:isbn:9514247191.

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Abstract The dissertation consists of three articles in which irrationality measures for some values of certain special cases of the Gauss hypergeometric function are considered in both archimedean and non-archimedean metrics. The first presents a general result and a divisibility criterion for certain products of binomial coefficients upon which the sharpenings of the general result in special cases rely. The paper also provides an improvement concerning th e values of the logarithmic function. The second paper includes two other special cases, the first of which gives irrationality measures

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Dumke, Jan Henrik Verfasser], Jörg [Akademischer Betreuer] [Brüdern, and Valentin [Akademischer Betreuer] Blomer. "Diophantine Equations in Many Variables / Jan Henrik Dumke. Gutachter: Jörg Brüdern ; Valentin Blomer. Betreuer: Jörg Brüdern." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2014. http://d-nb.info/1060543192/34.

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32

Abouzaid, Mourad. "Aspects effectifs d'analyse diophantienne." Bordeaux 1, 2006. http://www.theses.fr/2006BOR13196.

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Cette thèse traite de trois problèmes diophantiens distincts. Le premier chapitre est consacré à l’étude des diviseurs premiers de suites d’entiers connues sous le nom de nombres de Lucas et des nombres de Lehmer. Un théorème de Yu. BILU, G. HANROT et P. M. VOUTIER nous assure qu’à partir d’un certain rang (indépendent de la suite choisie, et explicite), tout nombre de Lucas (resp. De Lehmer ) admet un “nouveau” diviseur premier. Dans ce premier chapitre, nous complétons la liste des cas pathologiques commencée par P. M. VOUTIER d’une part et Yu. BILU, G. HANROT et P. M. VOUTIER d’autre part.

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33

Wodzak, Michael A. "Entire functions and uniform distribution /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9823328.

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34

Dehghan, Nezhad Akbar. "Equations cohomologiques de flots riemanniens et de difféomorphismes d'Anosov." Phd thesis, Université de Valenciennes et du Hainaut-Cambresis, 2006. http://tel.archives-ouvertes.fr/tel-00145138.

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Résumé: Dans cette thèse, on étudie les équations cohomologiques discrètes et continues dans les situations qui suivent.<br /> 1- Pour un champ de vecteurs X qui définit un feuilletage riemannien complet sur une variété M, on donne explicitement les conditions qui permettent de résoudre complètement l'équation cohomologique continue.<br /><br /> 2- Pour un champ X sur une la variété M obtenus (M et X) par suspension d'un difféomorphisme γ : N → N, on montre que l'équation cohomologique discrète du système dynamique discret (N, γ) est équivalente à l'équation cohomologique continue du système d

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35

Bartolomé, Boris Verfasser], Preda [Akademischer Betreuer] Mihăilescu, Yuri [Akademischer Betreuer] Bilu, Yann [Akademischer Betreuer] Bugeaud, Clemens [Akademischer Betreuer] Fuchs, and Jörg [Akademischer Betreuer] [Brüdern. "Diophantine Equations and Cyclotomic Fields / Boris Bartolomé. Betreuer: Preda Mihailescu ; Yuri Bilu. Gutachter: Yann Bugeaud ; Clemens Fuchs ; Jörg Brüdern." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2016. http://d-nb.info/1089093322/34.

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36

Al-Ghassani, Asma Said Ahmed. "Measures of growth of discrete rational equations." Thesis, Loughborough University, 2010. https://dspace.lboro.ac.uk/2134/6055.

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The general scope of this thesis is aimed at investigating certain classes of discrete equations through the analysis of certain characteristics of the solutions of these equations. We construct new methods of analysis based on the growth of these characteristics that let us single out known integrable discrete equations from certain class of equations. These integrable discrete equations are discrete analogues of the famous Painleve equations.

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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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38

Neto, Altino da Silva. "Convite às equações diofantinas: uma abordagem para a educação básica." Universidade Federal de Roraima, 2016. http://www.bdtd.ufrr.br/tde_busca/arquivo.php?codArquivo=343.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>Nesta dissertação, apresentamos os resultados de uma ampla pesquisa bibliográfica sobre as equações diofantinas e seus métodos de solução mais utilizados. A mais simples desta classe de equações é a da forma ax + by = c, com a, b e c números inteiros e ab 6= 0, chamada equação diofantina linear nas duas incógnitas x e y. No trabalho, expomos diversos métodos de resolução destas equações, em duas e três incógnitas. Para tanto, utilizamos conceitos de divisibilidade, divisão euclidiana, máximo divisor comum, números primos, dentre ou

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Souza, Romario Sidrone [UNESP]. "Equações diofantinas lineares, quadráticas e aplicações." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/149949.

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Submitted by ROMARIO SIDRONE DE SOUZA null (romario.sidrone@gmail.com) on 2017-03-22T13:09:53Z No. of bitstreams: 1 Equações Diofantinas Lineares, Quadráticas e Aplicações.pdf: 841142 bytes, checksum: 07c262b2dc6963eba6f51b8c68808746 (MD5)<br>Rejected by Luiz Galeffi (luizgaleffi@gmail.com), reason: Solicitamos que realize uma nova submissão seguindo a orientação abaixo: O arquivo submetido não contém o certificado de aprovação. O arquivo submetido está sem a ficha catalográfica. A versão submetida por você é considerada a versão final da dissertação/tese, portanto não poderá ocorre

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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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Hanley, Jodi Ann. "Egyptian fractions." CSUSB ScholarWorks, 2002. https://scholarworks.lib.csusb.edu/etd-project/2323.

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Egyptian fractions are what we know as unit fractions that are of the form 1/n - with the exception, by the Egyptians, of 2/3. Egyptian fractions have actually played an important part in mathematics history with its primary roots in number theory. This paper will trace the history of Egyptian fractions by starting at the time of the Egyptians, working our way to Fibonacci, a geologist named Farey, continued fractions, Diophantine equations, and unsolved problems in number theory.

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Синиця, О. О. "Нелінійні діофантові рівняння". Thesis, Сумський державний університет, 2018. http://essuir.sumdu.edu.ua/handle/123456789/66829.

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Нелінійним діофантовим рівнянням називається рівняння степінь якого не менший другого. Відмітимо, що загального алгоритму розв'язування діофантових рівнянь довільного степеня не існує, що було доведено Матіясевичем Ю. в 1970 році (10-та проблема Гільберта).

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Burns, Jonathan. "Recursive Methods in Number Theory, Combinatorial Graph Theory, and Probability." Scholar Commons, 2014. https://scholarcommons.usf.edu/etd/5193.

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Recursion is a fundamental tool of mathematics used to define, construct, and analyze mathematical objects. This work employs induction, sieving, inversion, and other recursive methods to solve a variety of problems in the areas of algebraic number theory, topological and combinatorial graph theory, and analytic probability and statistics. A common theme of recursively defined functions, weighted sums, and cross-referencing sequences arises in all three contexts, and supplemented by sieving methods, generating functions, asymptotics, and heuristic algorithms. In the area of number theory, this

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44

Khoshnoudirad, Daniel. "Aspects combinatoires des motifs linéaires en géométrie discrète." Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1046.

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La Géométrie Discrète, comme Science de l'Informatique Théorique, étudie notamment les motifs linéaires tels que les primitives discrètes apparaissant dans les images : les droites discrètes, les segments discrets, les plans discrets, les morceaux de plans discrets par exemple. Dans ce travail, je me concentre tout particulièrement sur les diagrammes de Farey qui apparaissent lors de l'étude des primitives discrètes que sont les (m,n)-cubes, autrement dit les morceaux de plans discrets. J’étudie notamment la Combinatoire des droites formant les diagrammes de Farey, en établissant des formules

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Capilheira, Bianca Herreira. "Equações diofantinas lineares : uma proposta para o Ensino Médio." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2012. http://hdl.handle.net/10183/62118.

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Este trabalho, cuja metodologia foi inspirada na Engenharia Didática, discute e investiga a viabilidade de inserir o ensino/estudo das equações diofantinas lineares no ensino médio. Foi desenvolvida e aplicada uma sequência didática em uma turma do 1º semestre do ensino médio integrado de química do Instituto Federal Sul-Rio-Grandense, Campus Pelotas. Através das atividades executadas pelos alunos, das anotações feitas pela mestranda e da filmagem de todas as aulas, foi possível coletar os dados sobre toda a experiência. Esta foi iniciada e baseada em um jogo nomeado “escova diofantina”, deriv

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Andres, Éric. "Cercles discrets et rotations discrètes." Université Louis Pasteur (Strasbourg) (1971-2008), 1992. http://www.theses.fr/1992STR13209.

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La synthèse d'images actuelles repose sur l'adaptation du monde continu au monde fini de l'ordinateur. La géométrie discrète, cadre de ces travaux, part du monde discret pour représenter le monde continu. Les algorithmes obtenues sont plus robustes. Nos travaux ont porté sur les cercles discrets et les rotations discrètes. Nous avons défini un nouveau cercle décrit par des équations diophantiennes, le cercle arithmétique. Le cercle arithmétique est une extension du cercle de Brasenham, il pave le plan et se trace grâce à un algorithme incrémental rapide. Une extension immédiate de ce cercle es

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Silva, Filardes de Jesus Freitas da. "Equações diofantinas classicas e aplicações." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307049.

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Orientador: Emerson Alexandre de Oliveira Lima<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-13T21:19:45Z (GMT). No. of bitstreams: 1 Silva_FilardesdeJesusFreitasda_M.pdf: 678989 bytes, checksum: 49b0b13ce88d8aa64141c17e237d85fe (MD5) Previous issue date: 2009<br>Resumo: Neste trabalho focalizamos os principais conceitos da teoria elementar dos números objetivando uma melhor compreensão das Equações Diofantinas Clássicas e suas aplicações e para isto explicitamos

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Barroso, de Freitas Nuno Ricardo. "Some Generalized Fermat-type Equations via Q-Curves and Modularity." Doctoral thesis, Universitat de Barcelona, 2012. http://hdl.handle.net/10803/91288.

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The main purpose of this thesis is to apply the modular approach to Diophantine equations to study some Fermat-type equations of signature (r; r; p) with r >/= 5 a fixed prime and “p” varying. In particular, we will study equations of the form x(r) + y(r) = Cz(p), where C is an integer divisible only by primes “q” is non-identical to 1; 0 (mod “r”) and obtain explicit arithmetic results for “r” = 5, 7, 13. We start with equations of the form x(5) + y(5) = Cz(p). Firstly, we attach two Frey curves E; F defined over Q(square root 5) to putative solutions of the equation. Then by using the

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Пальчик, О. О. "Комп'ютерна реалізація методів рішення діофантових рівнянь". Master's thesis, Сумський державний університет, 2018. http://essuir.sumdu.edu.ua/handle/123456789/72319.

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Реалізовано програмний засіб для рішення діофантового рівняння, розроблений на мові C# в середовищі програмування Microsoft Visual Studio Community 2017. Функціональне моделювання програмного засобу виконано на базі технології SADT. Проектування програмного продукту виконано в нотації UML.

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Campos, Adilson de. "EQUAÇÕES DIOFANTINAS LINEARES: POSSIBILIDADES DIDÁTICAS USANDO A RESOLUÇÃO DE PROBLEMAS." Universidade Federal de Santa Maria, 2015. http://repositorio.ufsm.br/handle/1/10945.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>This work presents an educational experiment carried out in a 9th grade class of elementary school, in order to assess the didactic and pedagogical possibilities involving the Linear Diophantine Equations theme, with the contextual support of Problem Solving. This application intends to expand the students' conceptions in arithmetic and algebra courses, also providing a concrete possibility of applicability of the greatest common divisor of two integers, a very neglected theme throughout the elementary school. In a level of element

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