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Mersenne Numbers And Fermat Numbers, Elena Deza


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Автор: Elena Deza
Название:  Mersenne Numbers And Fermat Numbers
ISBN: 9789811230318
Издательство: World Scientific Publishing
Классификация:
ISBN-10: 9811230315
Обложка/Формат: Hardback
Страницы: 328
Вес: 0.61 кг.
Дата издания: 24.08.2021
Серия: Selected chapters of number theory: special numbers
Язык: English
Размер: 211 x 150 x 13
Читательская аудитория: College/higher education
Ключевые слова: Number theory, MATHEMATICS / Combinatorics,MATHEMATICS / Geometry / Algebraic,MATHEMATICS / Number Theory
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Поставляется из: Англии
Описание:

This book contains a complete detailed description of two classes of special numbers closely related to classical problems of the Theory of Primes. There is also extensive discussions of applied issues related to Cryptography.


In Mathematics, a Mersenne number (named after Marin Mersenne, who studied them in the early 17-th century) is a number of the form Mn = 2n - 1 for positive integer n.


In Mathematics, a Fermat number (named after Pierre de Fermat who first studied them) is a positive integer of the form Fn = 2k+ 1, k=2n, where n is a non-negative integer.


Mersenne and Fermat numbers have many other interesting properties. Long and rich history, many arithmetic connections (with perfect numbers, with construction of regular polygons etc.), numerous modern applications, long list of open problems allow us to provide a broad perspective of the Theory of these two classes of special numbers, that can be useful and interesting for both professionals and the general audience.



Invitation to the Mathematics of Fermat-Wiles,

Автор: Yves Hellegouarch
Название: Invitation to the Mathematics of Fermat-Wiles,
ISBN: 0123392519 ISBN-13(EAN): 9780123392510
Издательство: Elsevier Science
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Цена: 67750.00 T
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Описание: Presents diverse concepts required to comprehend Fermat-Wiles` extraordinary proof. Placing these concepts in their historical context, this book contains several themes that could be developed by student research and numerous exercises and problems.

Harmonie Universelle

Автор: Marin Mersenne; Roger E. Chapman
Название: Harmonie Universelle
ISBN: 940175781X ISBN-13(EAN): 9789401757812
Издательство: Springer
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Цена: 102480.00 T
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Автор: O`Neil Mr Thomas
Название: The Grand Algorithm: A Mersenne Determinate Algorithm
ISBN: 1717420095 ISBN-13(EAN): 9781717420091
Издательство: Неизвестно
Цена: 102310.00 T
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Описание: Dear readers, This algorithm which I apply call The Grand Algorithm has been a life long pursuit of mine since I became involved with computers in the mid 1990's. There is a site which finds large Mersenne Primes named Gimps online. Yet the process of finding Mersenne primes through long trial factorization is a nightmare. Inside this book there is included two modules of python code. The first script is the Mersenne Determinate code and the second module is the Perfect Numbers code. Please download the Python shell; its free if you plan on using the code. If you check the code and type it correctly the numbers will role off at break neck speed. What you see is what you get, basically input and output. Is this statement true or is it an old adage for garbage in garbage out and do the results meet our expectations from cause and effect? We all utilize algorithms whether we know it or not. Bees with a brain the size of a pea utilize the "traveling sales man algorithm" which our computers devote many resources to figuring out. If you cook yes you use algorithms. So what is an algorithm? My simple definition is, "A procedure or steps which meet and end result". Most everything we do as humans require decisions and these choices effect the outcomes. In this book I will go on to describe my interest with Prime Numbers and what drove me to develop an algorithm which completely finds the true output of a Mersenne Prime Number A Mersenne prime is a perfect number where it can only be divided by 1 and itself. A mini-algorithm proves this to be true, 2 p-1, yet try doing this with pen and paper and you find with very large numbers you could take forever to find one guess for a prime number.

17 Lectures on Fermat Numbers

Автор: Michal Krizek; A. Solcova; Florian Luca; Lawrence
Название: 17 Lectures on Fermat Numbers
ISBN: 1441929525 ISBN-13(EAN): 9781441929525
Издательство: Springer
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Цена: 97820.00 T
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Описание: The pioneering work of French mathematician Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book was written in honor of the 400th anniversary of his birth, providing readers with an overview of the many properties of Fermat numbers and demonstrating their applications in areas such as number theory, probability theory, geometry, and signal processing. This book introduces a general mathematical audience to basic mathematical ideas and algebraic methods connected with the Fermat numbers.

Number Theory Related to Fermat`s Last Theorem

Автор: Koblitz
Название: Number Theory Related to Fermat`s Last Theorem
ISBN: 0817631046 ISBN-13(EAN): 9780817631048
Издательство: Springer
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Цена: 74530.00 T
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Modular Forms and Fermat`s Last Theorem

Автор: Gary Cornell; Joseph H. Silverman; Glenn Stevens
Название: Modular Forms and Fermat`s Last Theorem
ISBN: 0387989986 ISBN-13(EAN): 9780387989983
Издательство: Springer
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Цена: 69870.00 T
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Описание: Focuses on Andrew Wiles` proof of the Taniyama-Shimura-Weil conjecture for semistable elliptic curves and the works of Frey, Serre, Ribet showing that Wiles` Theorem would complete the proof of Fermat`s Last Theorem. This book reflects on the history of the problem. It describes the connections of Wiles` work with other parts of mathematics.

Ray Optics, Fermat`s Principle, and Applications to General Relativity

Автор: Volker Perlick
Название: Ray Optics, Fermat`s Principle, and Applications to General Relativity
ISBN: 3642086160 ISBN-13(EAN): 9783642086168
Издательство: Springer
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Цена: 104480.00 T
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From Fermat to Minkowski

Автор: W.K. B?hler; W. Scharlau; G. Cornell; H. Opolka
Название: From Fermat to Minkowski
ISBN: 1441928219 ISBN-13(EAN): 9781441928214
Издательство: Springer
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Цена: 48400.00 T
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Описание: Tracing the story from its earliest sources, this book celebrates the lives and work of pioneers of modern mathematics: Fermat, Euler, Lagrange, Legendre, Gauss, Fourier, Dirichlet and more. Includes an English translation of Gauss`s 1838 letter to Dirichlet.

Автор: Roshdi Rashed
Название: Histoire de l`analyse diophantienne classique: D`Abu Kamil a Fermat
ISBN: 3110337894 ISBN-13(EAN): 9783110337891
Издательство: Walter de Gruyter
Цена: 210690.00 T
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Описание: This is the first study of the history of Diophantine analysis and the theory of numbers from Ab? K?mil to Fermat (9th-17th century). It thus offers an elaborate and detailed overview on a fundamental chapter on classical mathematical thought and its relation to algebra and Diophantus’ Arithmetica.

Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties

Автор: Hiroshi Iritani, Todor Milanov, Yefeng Shen, Yongbin Ruan
Название: Gromov-Witten Theory of Quotients of Fermat Calabi-Yau Varieties
ISBN: 1470443635 ISBN-13(EAN): 9781470443634
Издательство: Mare Nostrum (Eurospan)
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Цена: 71060.00 T
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Histoire de l`analyse diophantienne classique: D`Abu Kamil a Fermat

Автор: Roshdi Rashed
Название: Histoire de l`analyse diophantienne classique: D`Abu Kamil a Fermat
ISBN: 3110336855 ISBN-13(EAN): 9783110336856
Издательство: Walter de Gruyter
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Цена: 161100.00 T
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Описание:

The series Scientia Graeco-Arabicais devoted to the study of scientific and philosophical texts from the Classical and the Islamic world handed down in Arabic. Through critical text editions and monographs it provides access to the topics of inquiry in which ancient science presented itself and developed over time in a continuous tradition between Antiquity and the modern period. All editions are accompanied by translations and philological and explanatory notes.

Languages of publication are English, German, French and Italian.


Ray Optics, Fermat`s Principle, and Applications to General Relativity

Автор: Volker Perlick
Название: Ray Optics, Fermat`s Principle, and Applications to General Relativity
ISBN: 3540668985 ISBN-13(EAN): 9783540668985
Издательство: Springer
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Цена: 121890.00 T
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Описание: This text on relativistic ray optics covers such topics as: light propagation in linear dielectric and permeable media; ray-optical structures on arbitrary manifolds; ray-optical structures on Lorentzian manifolds; and variational principles for rays.


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