ALGORITHMS FOR SOLVING LINEAR CONGRUENCES AND SYSTEMS OF LINEAR CONGRUENCES PDF Download
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Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 9
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Book Description
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences and we find the number of distinct solutions. Many examples of solving congruences are given.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 9
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Book Description
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences and we find the number of distinct solutions. Many examples of solving congruences are given.
Author: Andreas Dolzmann
Publisher:
ISBN:
Category : Congruences (Geometry)
Languages : en
Pages : 24
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Book Description
Abstract: "Based on an extended quantifier elimination procedure for discretely valued fields, we devise algorithms for solving multivariate systems of linear congruences over the integers. This includes determining integer solutions for sets of moduli which are all power of a fixed prime, uniform p-adic integer solutions for parametric prime power moduli, lifting strategies for these uniform p-adic solutions for given primes, and simultaneous lifting strategies for finite sets of primes. The method is finally extended to arbitrary moduli."
Author: FLORENTIN SMARANDACHE
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 8
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Book Description
In this section is presented a new integer number algorithm for linear equation. This algorithm is more “rapid” than W. Sierpinski’s presented in [1] in the sense that it reaches the general solution after a smaller number of iterations. Its correctness will be thoroughly demonstrated.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN: 1599730480
Category : Mathematics
Languages : en
Pages : 229
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Book Description
Articles, notes, generalizations, paradoxes, miscellaneous in mathematics, linguistics, and education.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 57
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Book Description
Two algorithms for solving Diophantine linear equations and five algorithms for solving Diophantine linear systems, together with many examples, are presented in this paper.
Author: William Stein
Publisher: Springer Science & Business Media
ISBN: 0387855254
Category : Mathematics
Languages : en
Pages : 173
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Book Description
This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 23
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Book Description
This chapter further extends the results obtained in chapters 4 and 5 (from linear equation to linear systems). Each algorithm is thoroughly proved and then an example is given.
Author: Henri Cohen
Publisher: Springer Science & Business Media
ISBN: 1441984895
Category : Mathematics
Languages : en
Pages : 591
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Book Description
Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.
Author: Richard Kipp Martin
Publisher: Springer Science & Business Media
ISBN: 1461549752
Category : Business & Economics
Languages : en
Pages : 739
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Book Description
This is a textbook about linear and integer linear optimization. There is a growing need in industries such as airline, trucking, and financial engineering to solve very large linear and integer linear optimization problems. Building these models requires uniquely trained individuals. Not only must they have a thorough understanding of the theory behind mathematical programming, they must have substantial knowledge of how to solve very large models in today's computing environment. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world problems. After presenting introductory material in Part I, Part II of this book is de voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projec tion. Through projection we take a system of linear inequalities and replace some of the variables with additional linear inequalities. Inverse projection, the dual of this process, involves replacing linear inequalities with additional variables. Fundamental results such as weak and strong duality, theorems of the alternative, complementary slackness, sensitivity analysis, finite basis the orems, etc. are all explained using projection or inverse projection. Indeed, a unique feature of this book is that these fundamental results are developed and explained before the simplex and interior point algorithms are presented.
Author: California Institute of Technology. Computer Science Department
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Book Description
