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Lee, Ellyn Jay. "Studies on diophantine equations". Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239075.
Pełny tekst źródłaMabaso, Automan Sibusiso. "Some exponential diophantine equations". Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85587.
Pełny tekst źródłaENGLISH 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.
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 Diophantiese vergelykings kan oplos nie. Die fokus van os studie is hoofsaaklik om eksponensiele Diophantiese vergelykings op te los met die modul^ere metode en met die metode van line^ere vorms in twee logaritmes.
Bartolomé, Boris. "Diophantine equations and cyclotomic fields". Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0104/document.
Pełny tekst źródłaThis thesis examines some approaches to address Diophantine equations, specifically we focus on the connection between the Diophantine analysis and the theory of cyclotomic fields.First, we propose a quick introduction to the methods of Diophantine approximation we have used in this research work. We remind the notion of height and introduce the logarithmic gcd.Then, we address a conjecture, made by Thoralf Skolem in 1937, on an exponential Diophantine equation. For this conjecture, let K be a number field, α1 ,…, αm , λ1 ,…, λm non-zero elements in K, and S a finite set of places of K (containing all the infinite places) such that the ring of S-integersOS = OK,S = {α ∈ K : |α|v ≤ 1 pour les places v ∈/ S}contains α1 , . . . , αm , λ1 , . . . , λm α1-1 , . . . , αm-1. For each n ∈ Z, let A(n)=λ_1 α_1^n+⋯+λ_m α_m^n∈O_S. Skolem suggested [SK1] :Conjecture (exponential local-global principle). Assume that for every non zero ideal a of the ring O_S, there exists n ∈ Z such that A(n) ≡0 mod a. Then, there exists n ∈ Z such that A(n)=0.Let Γ be the multiplicative group generated by α1 ,…, αm. Then Γ is the product of a finite abelian group and a free abelian group of finite rank. We prove that the conjecture is true when the rank of Γ is one.After that, we generalize a result previously published by Abouzaid ([A]). Let F(X,Y) ∈ Q[X,Y] be an irreducible Q-polynomial. In 2008, Abouzaid [A] proved the following theorem:Theorem (Abouzaid). Assume that (0,0) is a non-singular point of the plane curve F(X,Y) = 0. Let m = degX F, n = degY F, M = max{m, n}. Let ε satisfy 0 < ε < 1. Then for any solution (α,β) ∈ Q ̅2 of F(X,Y) = 0, we have eithermax{h(α), h(β)} ≤ 56M8ε−2hp(F) + 420M10ε−2 log(4M),ormax{|h(α) − nlgcd(α, β)|,|h(β) − mlgcd(α, β)|} ≤ εmax{h(α), h(β)}++ 742M7ε−1hp(F) + 5762M9ε−1log(2m + 2n)However, he imposed the condition that (0, 0) be a non-singular point of the plane curve F(X,Y) = 0. Using a somewhat different version of Siegel’s “absolute” lemma and of Eisenstein’s lemma, we could remove the condition and prove it in full generality. We prove the following theorem:Theorem. Let F(X,Y) ∈ Q ̅[X,Y] be an absolutely irreducible polynomial satisfying F(0,0)=0. Let m=degX F, n=degY F and r = min{i+j:(∂^(i+j) F)/(∂^i X∂^j Y)(0,0)≠0}. Let ε be such that 0 < ε < 1. Then, for all (α, β) ∈ Q ̅2 such that F(α,β) = 0, we have eitherh(α) ≤ 200ε−2mn6(hp(F) + 5)or|(lgcd(α,β))/r-h(α)/n|≤1/r (εh(α)+4000ε^(-1) n^4 (h_p (F)+log(mn)+1)+30n^2 m(h_p (F)+log(mn) ))Then, we give an overview of the tools we have used in cyclotomic fields. We try there to develop a systematic approach to address a certain type of Diophantine equations. We discuss on cyclotomic extensions and give some basic but useful properties, on group-ring properties and on Jacobi sums.Finally, we show a very interesting application of the approach developed in the previous chapter. There, we consider the Diophantine equation(1) Xn − 1 = BZn,where B ∈ Z is understood as a parameter. Define ϕ∗(B) := ϕ(rad (B)), where rad (B) is the radical of B, and assume that (2) (n, ϕ∗(B)) = 1.For a fixed B ∈ N_(>1)we let N(B) = {n ∈ N_(>1) | ∃ k > 0 such that n|ϕ∗(B)}. If p is an odd prime, we shall denote by CF the combined condition requiring thatI The Vandiver Conjecture holds for p, so the class number h+ of the maximal real subfield of the cyclotomic field Q[ζp ] is not divisible by p.II We have ir>(p) < √p − 1, in other words, there is at most √p − 1 odd integers k < p such that the Bernoulli number Bk ≡ 0 mod p. [...]
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.
Pełny tekst źródłaSmart, Nigel Paul. "The computer solution of diophantine equations". Thesis, University of Kent, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315089.
Pełny tekst źródłaLong, 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.
Pełny tekst źródłaBaczkowski, Daniel M. "Diophantine Equations Involving Arithmetic Functions of Factorials". Miami University / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=miami1088086258.
Pełny tekst źródłaAkhtari, Shabnam. "Thue equations and related topics". Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/1288.
Pełny tekst źródłaSchindler, 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.
Pełny tekst źródłaIbrahim, Mostafa. "Modular and reciprocity approaches to a family of diophantine equations". Thesis, University of Warwick, 2009. http://wrap.warwick.ac.uk/2761/.
Pełny tekst źródła蔡國光 i 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.
Pełny tekst źródłaKaminski, Lance. "A discussion of homogenous quadratic equations". Thesis, Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/1630.
Pełny tekst źródłaSmith, Jason. "Solvability characterizations of Pell like equations". [Boise, Idaho] : Boise State University, 2009. http://scholarworks.boisestate.edu/td/55/.
Pełny tekst źródłaMa, Fei Chun. "A Diophantine equations based cipher for Internet EDI security in Macau". Thesis, University of Macau, 1997. http://umaclib3.umac.mo/record=b1445591.
Pełny tekst źródłaChoi, 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.
Pełny tekst źródłaRen, 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.
Pełny tekst źródłaBeauchamp, 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.
Pełny tekst źródłaTitle 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.
Allen, Patrick. "Multiplicities of Linear Recurrence Sequences". Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2942.
Pełny tekst źródłaHeimonen, 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.
Pełny tekst źródłaDumke, Jan Henrik Verfasser], Jörg [Akademischer Betreuer] [Brüdern i 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.
Pełny tekst źródłaWodzak, Michael A. "Entire functions and uniform distribution /". free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9823328.
Pełny tekst źródłaBartolomé, Boris Verfasser], Preda [Akademischer Betreuer] Mihăilescu, Yuri [Akademischer Betreuer] Bilu, Yann [Akademischer Betreuer] Bugeaud, Clemens [Akademischer Betreuer] Fuchs i 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.
Pełny tekst źródłaAl-Ghassani, Asma Said Ahmed. "Measures of growth of discrete rational equations". Thesis, Loughborough University, 2010. https://dspace.lboro.ac.uk/2134/6055.
Pełny tekst źródłaMaximenko, Marianna. "Contribution au calcul de la solution générale d'équations en mots". Rouen, 1995. http://www.theses.fr/1995ROUE5003.
Pełny tekst źródłaNeto, 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.
Pełny tekst źródłaNesta 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 outros, que formam parte do currículo do Ensino Fundamental. No Brasil, as equações diofantinas não são comumente exploradas na Educação Básica, embora sejam perfeitamente compreensíveis nesse nível, como se mostra no texto do professor A. Guelfond, consultado na redação do trabalho. Na dissertação, incluímos, também, um capítulo sobre as contribuições de Diofanto para a Aritmética, que pode ser uma fonte de motivação para o estudo das equações diofantinas; e outro capítulo, ampliando as perspectivas sobre equações diofantinas não lineares. Esperamos que o trabalho seja uma fonte bibliográfica facilmente acessível aos professores da Educação Básica, e estimule seu interesse e criatividade para a introdução elementar desses conteúdos na prática docente e na preparação dos alunos para as Olimpíadas de Matemática.
In this dissertation, the results of a wide bibliographic research about Diophantine equations and their most used solution methods are exposed. The simplest equation of these class is the one in the form ax + by = c, with a, b and c integers numbers and ab 6= 0, called Diophantine linear equation in the unknowns x and y. Divers solutions methods for these equations, in two or three unknowns are discussed. Therefore, concepts like divisibility, Euclidean division, grated common divisor, prime numbers, among others, that are included in the Elementary Schools curriculum. In Brazil, Diophantine equations are not commonly exploited in Basic Education, even though they are perfectly understandable at this educational level, like Professor A. Guelfond shows in his book consulted in the redaction of the dissertation. There are also a chapter about Diophantuss contributions to Arithmetic, which can be a source of motivation to study the Diophantine equations; and another chapter, extending perspectives, about nonlinear Diophantine equations. We hope that the dissertation becomes a suitable easy accessible bibliographic font for Basic Education teachers and stimulates their interest and creativity for an elemental introducing of these contents in their teaching and in the students training for Math Olympiads.
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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Este trabalho é resultado de uma pesquisa bibliográfica sobre Diofanto e as equações que levam seu nome, as equações diofantinas. Mais especificamente, apresentamos as equações diofantinas lineares e alguns casos particulares das equações diofantinas quadráticas. Ainda, abordamos um estudo sobre alguns tópicos de teoria dos números e frações contínuas, afim de facilitar o entendimento sobre os teoremas e resultados acerca do tema central deste trabalho.
This work is the result of a bibliographical research about Diophantus and the equations that take his name, the Diophantine equations. More specifically, we present the linear diophantine equations and some particular cases of the quadratic diophantine equations. We have also studied topics about number theory and continuous fractions, in order to facilitate the understanding of theorems and results that are related to the central theme of this work.
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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The presente work aims to help students, teachers and lovers of mathematics, to better understand, interpret and solve problems that can be solved through Diophantine Equations. In this way, we present some basic concepts about Diophantine Equations as well as some practical applications. We also discuss Fermat ́s Last Theorem for the cases of n=2, n=3 and n=4, aiming to arouse interest, on the students, in Number Theory.
O presente trabalho tem como objetivo auxiliar estudantes, professores e apaixonados pela matemática, a melhor compreender, interpretar e resolver problemas que possam ser solucionados através das Equações Diofantinas. Desta forma, apresentamos alguns conceitos básicos sobre Equações Diofantinas bem como algumas aplicações práticas. Discutimos ainda, o Último Teorema de Fermat para os casos de n=2, n=3 e n=4, visando despertar o interesse no aluno pela teoria dos números.
Hanley, Jodi Ann. "Egyptian fractions". CSUSB ScholarWorks, 2002. https://scholarworks.lib.csusb.edu/etd-project/2323.
Pełny tekst źródłaСиниця, О. О. "Нелінійні діофантові рівняння". Thesis, Сумський державний університет, 2018. http://essuir.sumdu.edu.ua/handle/123456789/66829.
Pełny tekst źródłaBurns, Jonathan. "Recursive Methods in Number Theory, Combinatorial Graph Theory, and Probability". Scholar Commons, 2014. https://scholarcommons.usf.edu/etd/5193.
Pełny tekst źródłaBarroso, 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.
Pełny tekst źródłaEn esta tesis, utilizaremos el método modular para profundizar en el estudio de las ecuaciones de tipo (r; r; p) para r un primo fijado. Empezamos por utilizar la teoría de J. Quer sobre variedades abelianas asociadas con Q-curvas y embedding problems para producir dos curvas de Frey asociadas con hipotéticas soluciones de infinitas ecuaciones de tipo (5; 5; p). Después, utilizando la conjetura de Serre y el método multi-Frey de Siksek demostraremos que las hipotéticas soluciones no pueden existir. Describiremos también un método general que nos permite atacar un número infinito de ecuaciones de tipo (r; r; p) para cada primo “r” mayor o igual que 7. El método hace uso de curvas elípticas sobre cuerpos de números, teoremas de modularidad, teoremas de bajada de nivel y formas modulares de Hilbert. Además, para ecuaciones de tipo (7; 7; p) y (13; 13; p) calcularemos los espacios de formas modulares relevantes y demostraremos que una familia infinita de ecuaciones no admite cierto tipo de soluciones. Además, demostraremos un nuevo teorema de modularidad para curvas elípticas sobre cuerpos totalmente reales abelianos. Finalmente, para primos congruentes con 1 módulo 4 propondremos dos curvas de Frey más. Demostraremos que son “k-curves” (una generalización de Q-curva) y también que satisfacen las propiedades necesarias para que pueda ser útiles en la aplicación del método modular.
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.
Pełny tekst źródłaThis work, whose methodology is inspired by didactical engineering, discusses and investigates the viability of introducing linear diophantine equations at High School level study and teaching. We developed and applied a didactical sequence to a first semester chemistry oriented high school at the Pelotas campus of the Sul-Rio-Grandense Federal Institute. We collected the data of this whole experience, starting with all the activities performed by the students and continuing with notes taken by the author as well as the whole class footage. We started the seminars with a card game that we called “diophantine escova”, derived from the usual “escova” card game. We followed it by structured activities with exercises and several debates that led the students, in a natural way, to understand the definitions, concepts and results about Diophantine Equations. The didactical sequence we have created had very clear and specific goals in each activity. When the seminars ended, we analyzed and reformulated the sequence and therefore, in Appendix C, we present a totally improved and ready to use sequence for any teacher interested in developing linear diophantine equations in high school. The data analysis indicated that fist year high school students have the necessary mathematical skills to understand all concepts and results of basic linear diofantine equations.
Silva, Filardes de Jesus Freitas da. "Equações diofantinas classicas e aplicações". [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307049.
Pełny tekst źródłaDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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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 os conceitos de Números primos, Algoritmo de Euclides, Máximo divisor comum e Mínimo múltiplo comum, assim como a teoria das Congruências, uma abordagem sobre a Criptografica RSA e Soma de Inteiros. Palavras-Chave: Congruências Lineares, Soma de Inteiros, Equação de Fermat, Soma de Quadrados
Abstract: In this work we focus the main concepts of the elementary theory of numbers seeking a better understanding of Classical diophantine equations and their applications for this and explained the concepts of prime numbers, algorithms of Euclid, maximum common divisor and least common multiple and the theory of congruence , an approach on the RSA encryption and Sum of Integers. Keywords: Linear congruence, Sum of Integers, equation of Fermat, Sum of Squares
Mestrado
Teoria dos Numeros
Mestre em Matemática
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.
Pełny tekst źródłaKhoshnoudirad, Daniel. "Aspects combinatoires des motifs linéaires en géométrie discrète". Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1046.
Pełny tekst źródłaDiscrete Geometry, as Theoretical Computer Science, studies in particular linear patterns such as discrete primitives in images: the discrete lines, discrete segments, the discrete planes, pieces of discrete planes, for example. In this work, I particularly focused on Farey diagrams that appear in the study of the $ (m, n) $ - cubes, ie the pieces of discrete planes. Among others, I study the Combinatorics of the Farey lines forming diagram Farey, establishing exact formulas. I also get an asymptotic estimate using Combinatorial Number Theory. Then, I get a lower bound for the cardinality of the Farey vertices. After that, we analyze the strategies used in the literature for the study of (m, n)- cubes only by Farey diagrams in two dimensions. In order to get new and more accurate bounds for (m, n)- cubes, one of the few available methods, is to propose a generalization for the concept of preimage of a discrete segment for (m, n) - cube, resulting in a new combinatorial inequality. Thus, we introduce the notion Farey diagram in three dimensions
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.
Pełny tekst źródłaThis 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 elementary school, one of the main vehicles that allows you to work the initiative, creativity and exploring spirit is through Problem Solving. A Mathematics Teacher has a great opportunity to challenge the curiosity of the students by presenting them problems that are compatible with their knowledge and guiding them through incentive questions and this teacher can also try to input on them a taste for discovery and independent thinking. Thus, a very reasonable way is to prepare the student to deal with new situations, whatever they may be. The paper is organized in three chapters. In the first chapter entitled "Problem Solving in mathematics teaching" a theoretical foundation on the Teaching of Problem Solving is searched based on the Hungarian-American author George Polya and Luiz Roberto Dante and, it also presents some aspects from the learning theory proposed by Vygotsky. In the second chapter entitled "arithmetic concepts" the themes treated are: Greatest Common Divisor (gcd), Euclidean algorithm, Bèzout theorem and Linear Diophantine Equations. In the third and final chapter entitled "pedagogical experimentation" as mentioned above, the experimentation in a class of ninth grade of an elementary school. This experiment is based on the Didactic Engineering methodology, comprising the following stages: theme and scope of action; previous analyzes associated with the dimensions: epistemological, didactic and cognitive; prior analysis; experimentation; aftermost analysis and validation of Didactic Engineering.
Este trabalho apresenta uma experimentação pedagógica realizada numa turma de 9ºano do Ensino Fundamental com o objetivo de aferir as possibilidades didático-pedagógicas envolvendo a temática Equações Diofantinas Lineares, tendo como suporte contextual a Resolução de Problemas. Tal aplicação tem o intento de ampliar as concepções dos alunos nos campos da aritmética e da álgebra, dando também uma possibilidade concreta de aplicabilidade do máximo divisor comum de dois números inteiros, tema tão negligenciado ao longo do Ensino Fundamental. Em um nível de Ensino Fundamental, um dos principais veículos que permite trabalhar a iniciativa, a criatividade e o espírito explorador é a Resolução de Problemas. O professor de Matemática tem, dessa forma, uma grande oportunidade de desafiar a curiosidade de seus alunos, apresentando-lhes problemas compatíveis com os conhecimentos destes e orientando-os através de indagações incentivadoras, podendo incutir-lhes o gosto pela descoberta e pelo raciocínio independente. Assim, um caminho bastante razoável é preparar o aluno para lidar com situações novas, quaisquer que sejam elas. O trabalho está organizado em três capítulos. No primeiro capítulo intitulado A Resolução de Problemas no ensino da Matemática busca-se uma fundamentação teórica sobre a Didática da Resolução de Problemas no autor húngaro-americano George Polya e Luiz Roberto Dante e, também, são apresentados alguns aspectos da teoria da aprendizagem proposta por Vygotsky. No segundo capítulo intitulado conceitos de aritmética são tratados os temas: Máximo Divisor Comum (mdc), Algoritmo de Euclides, Teorema de Bèzout e Equações Diofantinas Lineares. No terceiro e último capítulo intitulado experimentação pedagógica é apresentada a experimentação supracitada numa turma de nono ano do Ensino Fundamental. Tal experimentação é baseada na metodologia Engenharia Didática, compreendendo os seguintes momentos: tema e campo de ação; análises prévias associadas às dimensões: epistemológica, didática e cognitiva; análise a priori; experimentação; análise a posteriori e validação da Engenharia Didática.
Nascimento, NatÃlia Medeiros do. "EquaÃÃes diofantinas e o mÃtodo das secantes e tangentes de Fermat". Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=12409.
Pełny tekst źródłaAo longo das Ãltimas dÃcadas, a transmissÃo do conhecimento matemÃtico na EducaÃÃo BÃsica sofreu diversas mudanÃas. âO Ensino Tradicionalâ da matemÃtica era baseado na memorizaÃÃo de fÃrmulas, havendo assim uma mecanizaÃÃo no processo de resoluÃÃo de problemas, onde o discente era visto como um ser passivo. A nova visÃo de ensino, que busca significar o que conteÃdo exposto em sala, motivou a escolha desse tema, visto que situaÃÃes problemas envolvendo equaÃÃes diofantinas podem ser facilmente percebidas em nosso cotidiano. O objetivo deste trabalho à oportunizar a realizaÃÃo de uma leitura consultiva para o professor do Ensino BÃsico, e asseverar que essas equaÃÃes podem ser aplicadas na EducaÃÃo BÃsica como uma ferramenta que instiga o pensamento lÃgico, o raciocÃnio, a compreensÃo e a interpretaÃÃo matemÃtica. A formulaÃÃo desse material que està dividido em cinco capÃtulos se deu atravÃs de levantamento bibliogrÃfico por meio de pesquisas descritivas. A introduÃÃo compÃe o primeiro capÃtulo. O segundo capÃtulo versa sobre o Legado de Diofanto: vida e obras, ressaltando sua obra titulada âArithmeticaâ que contribuiu significativamente para o desenvolvimento da teoria dos nÃmeros. O terceiro capÃtulo trata das equaÃÃes diofantinas lineares de n variÃveis. O quarto capÃtulo aborda as ternas itagÃricas, o MÃtodo das Secantes e Tangentes de Fermat na busca de soluÃÃes racionais para quaÃÃes, com coeficientes racionais, da forma ax2+by2 = c, e um caso particular do Ãltimo Teorema de Fermat. O quinto capÃtulo à composto de problemas sobre equaÃÃes diofantinas lineares.
Over the past decades, the transmission of mathematical knowledge in basic education has undergone several changes. The âTeaching Traditionalâ math was based on memorizing formulas, so there mechanization in problem solving where the student was seen as a liability to be process. The new vision of education that seeks to signify exposed to room content, motivated the choice of this theme, as diophantine equations involving situations problems can be easily noticed in our daily lives. The objective of this work is an opportunity for a realization of an advisory reading for the teacher of basic education, and assert that these equations can be applied in basic education as a tool that encourages the logical thinking, reasoning, understanding and mathematical interpretation. The formulation of this material which is divided into five chapters was through literature review through descriptive research. The introduction comprises the first chapter. The second chapter deals with the Legacy of Diophantus: life and works, emphasizing his work entitled âArithmeticaâ which contributed significantly to the development of number theory. The third chapter deals with linear Diophantine equations in n variables. The fourth chapter discusses the Pythagorean tender, Fermatâs of secants and Tangents method, in finding rational solutions to equations with rational coefficients, of the form ax2 + by2 = c and a particular case Fermatâs Last Theorem. The fifth chapter is composed of problems on linear diophantine equations.
Dantas, Joice de Andrade. "De solutione problematum diophanteorum per n?meros integros : o primeiro trabalho de Euler sobre equa??es diofantinas". Universidade Federal do Rio Grande do Norte, 2011. http://repositorio.ufrn.br:8080/jspui/handle/123456789/14500.
Pełny tekst źródłaThe present dissertation analyses Leonhard Euler?s early mathematical work as Diophantine Equations, De solutione problematum diophanteorum per n?meros ?ntegros (On the solution of Diophantine problems in integers). It was published in 1738, although it had been presented to the St Petersburg Academy of Science five years earlier. Euler solves the problem of making the general second degree expression a perfect square, i.e., he seeks the whole number solutions to the equation ax2+bx+c = y2. For this purpose, he shows how to generate new solutions from those already obtained. Accordingly, he makes a succession of substitutions equating terms and eliminating variables until the problem reduces to finding the solution of the Pell Equation. Euler erroneously assigns this type of equation to Pell. He also makes a number of restrictions to the equation ax2+bx+c = y and works on several subthemes, from incomplete equations to polygonal numbers
Nesta pesquisa analisamos historicamente e matematicamente o primeiro trabalho de Leonhard Euler sobre Equa??es Diofantinas o De solutione problematum diophanteorum per n?meros integros ( Sobre a solu??o de problemas diofantinos por n?meros inteiros ). Foi publicado em 1738, embora apresentado ? Academia de S?o Petersburgo cinco anos antes. No texto, Euler trata do problema de fazer com que a express?o generalizada do segundo grau seja igual a um quadrado perfeito, isto ?, procura solu??es no conjunto dos n?meros inteiros para equa??o ax2+bx+c = y2. Para tanto, Euler mostra como descobrir mais solu??es depois que uma primeira ? encontrada, fazendo uma s?rie de substitui??es combinando termos e eliminando vari?veis, at? que o trabalho se resume a encontrar a solu??o para ,q=ⱱap?+1 uma equa??o de Pell. Este trabalho ? o primeiro tamb?m em que Euler atribui erroneamente esse tipo de equa??o a Pell. Euler faz tamb?m, uma s?rie de restri??es para a equa??o ax2+bx+c = y2 e trabalha com diversos subcasos, que v?o desde equa??es incompletas at? o trabalho com n?meros poligonais
Alcántara, Bode Julio. "Some Properties of the Beurling Correlation Function". Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97055.
Pełny tekst źródłaPRAZERES, Sidmar Bezerra dos. "O Teorema chinês dos restos e a partilha de senhas". Universidade Federal Rural de Pernambuco, 2014. http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/6709.
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This paper aims to show the reader the importance of some topics of Number Theory. Work here, and prerequisites (Euclid Algorithms, Divisibility, Maxim Common Divisor), content with Linear Diophantine equations, congruences, and the main theme, which is the mighty Chinese Remainder Theorem of presenting their theories, importance, applicability on the day and its usefulness in the Theory of Numbers. The main applicability of Chinese Remainder Theorem of this work is Sharing Passwords. Sharing of passwords is a security mechanism, where a certain amount of people take possession of a key to access the secret without the possibility of obtaining the secret with his own key.
Este trabalho tem como objetivo mostrar ao leitor a importância de alguns t ópicos da Teoria dos N úmeros. Trabalharemos aqui, al ém de pré-requisitos (Algoritmo de Euclides, Divisibilidade, M áximo Divisor Comum), conte údos como Equa ções Diofantinas Lineares, Congruências e o principal tema, que e o poderoso Teorema Chinês dos Restos, apresentando suas teorias, importâncias, aplicabilidade no dia a dia e sua a utilidade na Teoria dos N úmeros. A principal aplicabilidade do Teorema Chinês apresentada neste trabalho e a Partilha de Senhas. Esta partilha de senhas é um mecanismo de seguran ça, onde uma certa quantidade de pessoas tomam posse de uma chave de acesso sem a possibilidade de obter a senha principal com a sua pr ópria chave.
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.
Pełny tekst źródłaHaristoy, Julien. "Equations diophantiennes exponentielles". Université Louis Pasteur (Strasbourg) (1971-2008), 2003. http://www.theses.fr/2003STR13123.
Pełny tekst źródłaNguyen, Phu Qui Pierre. "Equations de Mahler et hypertranscendance". Paris 6, 2012. http://www.theses.fr/2012PA066809.
Pełny tekst źródłaLet K be a field equipped with an endomorphism \sigma. In this thesis, we show that the Galois theory for \sigma-difference equations, well known if \sigma is an automorphism of K, can be adapted to the case when \sigma is not necessarily surjective anymore, by passing to the inversive closure of K. We then use this Galois theory to give an algebraic independence criterion for solutions of first order \sigma-equations. This result allows us to characterize the hyperalgebraic solutions of such \sigma-equations when K is endowed with a derivation which almost commutes with \sigma. Applying our algebraic independence criterion to the Mahler operator setting, we give a galoisian proof of a hypertranscendence theorem of Ke. Nishioka
Borges, Fábio Vieira de Andrade. "Equações diofantinas lineares em duas incógnitas e suas aplicações". Universidade Federal de Goiás, 2013. http://repositorio.bc.ufg.br/tede/handle/tede/3124.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The main objective of this assignment is to help students and also teachers with the resolution and understanding of problems involving the Linear Diophantine Equations with Two Incognits through the elaboration and application of didactic activities in order to contribute to the study of this kind of equations. Through the tasks it was aimed to dothe integration of Arithmetic with Algebra and Geometry by using some computational programs which worked as support to the graphical visualization of the entire solutions. In the first chapters the essence of the Elementary Theory of Numbers will be better known, since the mathematical tools which will be used to solve linear Diophantine equations will be displayed and demonstrated, some of them already known, like the greatest common divisor (g.d.c). Then the Diophantine equations and theirapplication methods for the solution of daily problems will be introduced. The Conclusion of this study highlights the importance of algebraic and geometric interpretation of Linear Diophantine Equations, and also emphasizes that the contact with problems of this area contributes to the students reasoning abilities development in a creative way. It is important to emphasize that this issue can be introduced in high school.
O presente trabalho tem como objetivo principal auxiliar os alunos e professores na resolução e compreensão de problemas envolvendo as Equações Diofantinas Lineares com Duas Incógnitas através da elaboração e aplicação de atividades didáticas destinadas a contribuir para o estudo desse tipo de equações. Procurou-se nas tarefas fazer a integração da Aritmética com a Álgebra e a Geometria, utilizando-se de alguns programas computacionais que serviram de suporte para as visualizações gráficas das soluções inteiras. Nos primeiros capítulos vamos conhecer melhor a essência da Teoria Elementar dos Números, pois apresentaremos e demonstraremos as ferramentas matemáticas que serão utilizadas na resolução das Equações Diofantinas Lineares, algumas delas já conhecidas, que é o caso do máximo divisor comum (m.d.c). Em seguida serão introduzidas as equações diofantinas e os métodos de determinação de soluções da mesma para aplicação em resolução de problemas do cotidiano. A conclusão desse trabalho ressalta a importância da interpretação algébrica e geométrica das Equações Diofantinas Lineares, e que o contato com problemas desta área contribui para que o aluno desenvolva, de forma criativa suas habilidades de raciocínio. É importante enfatizar que esse tema pode ser abordado no Ensino Médio.
Hanine, El Mostafa. "Equations diophantiennes p-adiques et congruences modulo p2". Toulouse 3, 1990. http://www.theses.fr/1990TOU30088.
Pełny tekst źródłaRahimi, Shahriar. "A NOVEL LINEAR DIOPHANTINE EQUATION-BAESD LOW DIAMETER STRUCTURED PEER-TO-PEER NETWORK". OpenSIUC, 2017. https://opensiuc.lib.siu.edu/dissertations/1462.
Pełny tekst źródłaСиниця, О. "Методи розв'язування діофантових рівнянь". Thesis, Cумський державний університет, 2016. http://essuir.sumdu.edu.ua/handle/123456789/48885.
Pełny tekst źródłaAbouzaid, Mourad. "Aspects effectifs d'analyse diophantienne". Bordeaux 1, 2006. http://www.theses.fr/2006BOR13196.
Pełny tekst źródłaDehghan, 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.
Pełny tekst źródła1- 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.
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 dynamique continu (M, X) .
3- Dans le cas où la variété M est le quotient TAⁿ⁺¹du groupe de Lie G=ℝⁿ ⋊A ℝ par le réseau Γ=ℤⁿ ⋊Aℤ avec A ∈SL(n,ℤ)
hyperbolique à valeurs propres réelles positives et X l'élément de l'algèbre de Lie Ģ de G qui induit le flot d'Anosov ℱ sur TAⁿ⁺¹,on donne explicitement les solutions des deux équations en question ainsi que d'autres invariants géométriques qui leur sont associés notamment la cohomologie feuilletée de ℱ et les distrbutions A-invariantes
Валенкевич, М. Є. "Діофантові рівняння". Thesis, Сумський державний університет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/38857.
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