The Algorithmic Resolution of Diophantine Equations PDF Download

Author: Nigel P. Smart
Publisher: Cambridge University Press
ISBN: 9780521646338
Category : Mathematics
Languages : en
Pages : 264

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Book Description
A coherent account of the computational methods used to solve diophantine equations.

Author: Nigel P. Smart
Publisher:
ISBN: 9781107095366
Category : Diophantine equations
Languages : en
Pages : 260

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Book Description
A coherent account of the computational methods used to solve diophantine equations.

Author: Nigel Paul Smart
Publisher:
ISBN: 9781107089150
Category : MATHEMATICS
Languages : en
Pages : 262

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Book Description
A coherent account of the computational methods used to solve diophantine equations.

Author: Benne M. M. De Weger
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 232

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Book Description

Author: István Gaál
Publisher: Springer Nature
ISBN: 3030238652
Category : Mathematics
Languages : en
Pages : 326

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Book Description
Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.

Author: Istvan Gaal
Publisher: Springer Science & Business Media
ISBN: 1461200857
Category : Mathematics
Languages : en
Pages : 192

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Book Description
Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.

Author: Octavian Cira
Publisher: Infinite Study
ISBN: 1599733072
Category : Diophantine equations
Languages : en
Pages : 254

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Book Description
In this book a multitude of Diophantine equations and their partial or complete solutions are presented. How should we solve, for example, the equation η(π(x)) = π(η(x)), where η is the Smarandache function and π is Riemann function of counting the number of primes up to x, in the set of natural numbers? If an analytical method is not available, an idea would be to recall the empirical search for solutions. We establish a domain of searching for the solutions and then we check all possible situations, and of course we retain among them only those solutions that verify our equation. In other words, we say that the equation does not have solutions in the search domain, or the equation has n solutions in this domain. This mode of solving is called partial resolution. Partially solving a Diophantine equation may be a good start for a complete solving of the problem. The authors have identified 62 Diophantine equations that impose such approach and they partially solved them. For an efficient resolution it was necessarily that they have constructed many useful ”tools” for partially solving the Diophantine equations into a reasonable time. The computer programs as tools were written in Mathcad, because this is a good mathematical software where many mathematical functions are implemented. Transposing the programs into another computer language is facile, and such algorithms can be turned to account on other calculation systems with various processors.

Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1107097606
Category : Mathematics
Languages : en
Pages : 381

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Book Description
A comprehensive, graduate-level treatment of unit equations and their various applications.

Author: Jorn Steuding
Publisher: CRC Press
ISBN: 1584884827
Category : Mathematics
Languages : en
Pages : 275

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Book Description
While its roots reach back to the third century, diophantine analysis continues to be an extremely active and powerful area of number theory. Many diophantine problems have simple formulations, they can be extremely difficult to attack, and many open problems and conjectures remain. Diophantine Analysis examines the theory of diophantine approximations and the theory of diophantine equations, with emphasis on interactions between these subjects. Beginning with the basic principles, the author develops his treatment around the theory of continued fractions and examines the classic theory, including some of its applications. He also explores modern topics rarely addressed in other texts, including the abc conjecture, the polynomial Pell equation, and the irrationality of the zeta function and touches on topics and applications related to discrete mathematics, such as factoring methods for large integers. Setting the stage for tackling the field's many open problems and conjectures, Diophantine Analysis is an ideal introduction to the fundamentals of this venerable but still dynamic field. A detailed appendix supplies the necessary background material, more than 200 exercises reinforce the concepts, and engaging historical notes bring the subject to life.

Author: R. C. Mason
Publisher: Cambridge University Press
ISBN: 9780521269834
Category : Mathematics
Languages : en
Pages : 142

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Book Description
A self-contained account of a new approach to the subject.