Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 24 for “"Diophantine equations"”.
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The Algorithmic Solution of Simultaneous Diophantine Equations
… is presented for solving pairs of simultaneous Diophantine equations, such as those which result from the 2-descent process on elliptic curves. The method works by determining a set of solutions modulo a prime P, raising each of these solutions to a set of P solutions modulo p2, and then …
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Nonexistence of Solutions to Certain Families of Diophantine Equations
<p>In this work, I examine specific families of Diophantine equations and prove that they have no solutions in positive integers. The proofs use a combination of classical elementary arguments and powerful tools such as Diophantine approximations, Lehmer numbers, the modular approach, and earlier …
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Incompatibility of Diophantine Equations Arising from the Strong Factorial Conjecture
The Strong Factorial conjecture was recently formulated by Arno van den Essen and Eric Edo. The problem is motivated by several outstanding problems including the Jacobian, Image, and Vanishing conjectures. In this defense, we discuss how the conjecture can be reformulated in terms of systems of …
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Arithmetic statistics of algebraic groups
… of solutions to certain families of multivariate Diophantine equations. This thesis is organised into two main parts. The first part focuses on the arithmetic statistics of integer and rational matrices. More precisely, the topics considered in this part include the statistics of product sets of …
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Improving regulator verification and compact representations in real quadratic fields
The study of Diophantine equations, and in particular the erroneously-named Pell equation, has a long and intriguing history. In this work, we investigate solutions to the Pell equation and to a closely related quantity called the fundamental unit. Though it is somewhat simple to show these …
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Products in Lambda-Rings
… for special cases, to solving a system of linear Diophantine equations in a distinguished region of space.
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Unification and equation solving in nilpotent groups and monoids
… the solutions of a certain restricted class of diophantine equations of degree k. The unification problem for the theories of nilpotent groups of class Z5 is shown to be undecidable. This improves the result of Romankov [60] who showed it for class Z 9. The result is established by reducing the …
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The Tarry -Escott Problem Over Quadratic Fields
… study the Tarry-Escott problem and some related diophantine systems over Z and over some quadratic fields. We give infinitely many solutions of the Tarry-Escott problem over Zi of degrees 2, 3, 4, 5 and 7, none of which can be directly derived from solutions over Z . We show that there are …
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A discussion of homogenous quadratic equations
This thesis will look at Quadratic Diophantine Equations. Some well known proofs, including how to compute all Pythagorean triples and which numbers can be represented by the sum of two and four squares will be presented. Some concepts that follow from these theorems will also be presented. These …
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The discriminant — From a quadratic equation to dynamic nonlinear systems
… the Quadratic Formula to solve quadratic equations, students learn its use for the classification of type and number of solutions for each equation being solved. Most students memorize the formula, identify the correct values for each variable, and successfully solve to find solutions for …
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Power Integral Points on Elliptic Curves
… of the modern approaches towards the solution of Diophantine equations, and utilizes them to display the nonexistence of perfect powers occurring in certain types of sequences. In particular we look at the denominator divisibility sequences (Bn) formed by Mordell elliptic curves ED : y2 = x3+D. …
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On Weak Number Theories
… 1 we reformulate Schinzel's theorem about diophantine equations with parameters to get some number theoretic results. In later chapter we apply these results to solve various decidability and definability problems. In Chapter 2 we prove that (FOR ALL)('n)(THERE EXISTS) over Z is decidable, …
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Archimedo „problema bovinum" ir Pelio lygtys /
Archimedes’ Problema Bovinum and Pell’s Equations The aim of this thesis is to discuss Pell's equation and its link to Archimedes' Problema Bovinum. First chapter introduces to Diophantine equations, while providing examples on various cases that famous mathematicians stood upon. In the begining of …
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ΠΡΩΤΟΙ ΑΡΙΘΜΟΙ ΚΑΙ ΚΥΚΛΟΤΟΜΙΑ-ΠΡΩΤΟΙ ΑΡΙΘΜΟΙ ΤΗΣ ΜΟΡΦΗΣ Χ + (Χ+1)
… INTEGRAL SOLUTIONS OF THE FOLLOWING FAMILY OF DIOPHANTINE EQUATIONS OF FERMAT TYPE: (FK) X2- 2Y2=2K2-1, K=0,1,2,... . THUS THE STUDY OF EQUATION (*) IS REDUCED TO THE STUDY OF THE FAMILY OF EQUATIONS (FK) IN TERMS OF GAUSS TYPE TRANSFORMATIONS. FINALLY, ALL COMPOSITE NUMBERS OF THE FORM …
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Linear Forms in Logarithms and Fibonacci Numbers
… the supervision of Omar Kihel, pertaining to Diophantine triples of Fibonacci numbers. To go along with this will be introductory material not included in said paper which establishes the mathematical concepts therein and offers some historical perspective and motivation. The initial aim of …
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Approximations by means of continued fractions
… in other investigations, chiefly the solution of Diophantine equations. Advances are announced from time to time in special areas of the field. The equivalence of continued fractions to infinite products and to series expansions was recognised early in their study. Series expansions proved most …
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Error-Correcting Codes Associated With Generalized Hadamard Matrices Over Groups
… ptn</em>) do not exist. By analyzing quadratic Diophantine equations, new methods for constructing such parameter sequences are obtained. These results show the rich number theoretic complexity of the existence question for generalized Hadamard matrices.</p>
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New techniques for implementing membrane systems
… in this thesis use solutions of linear system Diophantine equations, data structures (virtual or physical) and probabilistic and statistical patterns. Este tesis se encuadra en computacion biomolecular y de una manera mas especifica en el area de las propiedades de las celulas vivas. Este area …
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