ANOTHER INTEGER NUMBER ALGORITHM TO SOLVE LINEAR EQUATIONS (USING CONGRUENCY) PDF Download
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Author: Florentin Smarandache Publisher: Infinite Study ISBN: Category : Languages : en Pages : 7
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 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: Category : Languages : en Pages : 7
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 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: Category : Languages : en Pages : 8
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: Category : Languages : en Pages : 9
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 : 57
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: FLORENTIN SMARANDACHE Publisher: Infinite Study ISBN: Category : Languages : en Pages : 6
Book Description
An algorithm is given that ascertains whether a linear equation has integer number solutions or not; if it does, the general integer solution is determined.
Author: Florentin Smarandache Publisher: Infinite Study ISBN: Category : Languages : en Pages : 23
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: Oscar Levin Publisher: Createspace Independent Publishing Platform ISBN: 9781724572639 Category : Languages : en Pages : 238
Book Description
Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.
Author: Ellina Grigorieva Publisher: Birkhäuser ISBN: 3319909150 Category : Mathematics Languages : en Pages : 405
Book Description
Through its engaging and unusual problems, this book demonstrates methods of reasoning necessary for learning number theory. Every technique is followed by problems (as well as detailed hints and solutions) that apply theorems immediately, so readers can solve a variety of abstract problems in a systematic, creative manner. New solutions often require the ingenious use of earlier mathematical concepts - not the memorization of formulas and facts. Questions also often permit experimental numeric validation or visual interpretation to encourage the combined use of deductive and intuitive thinking. The first chapter starts with simple topics like even and odd numbers, divisibility, and prime numbers and helps the reader to solve quite complex, Olympiad-type problems right away. It also covers properties of the perfect, amicable, and figurate numbers and introduces congruence. The next chapter begins with the Euclidean algorithm, explores the representations of integer numbers in different bases, and examines continued fractions, quadratic irrationalities, and the Lagrange Theorem. The last section of Chapter Two is an exploration of different methods of proofs. The third chapter is dedicated to solving Diophantine linear and nonlinear equations and includes different methods of solving Fermat’s (Pell’s) equations. It also covers Fermat’s factorization techniques and methods of solving challenging problems involving exponent and factorials. Chapter Four reviews the Pythagorean triple and quadruple and emphasizes their connection with geometry, trigonometry, algebraic geometry, and stereographic projection. A special case of Waring’s problem as a representation of a number by the sum of the squares or cubes of other numbers is covered, as well as quadratic residuals, Legendre and Jacobi symbols, and interesting word problems related to the properties of numbers. Appendices provide a historic overview of number theory and its main developments from the ancient cultures in Greece, Babylon, and Egypt to the modern day. Drawing from cases collected by an accomplished female mathematician, Methods in Solving Number Theory Problems is designed as a self-study guide or supplementary textbook for a one-semester course in introductory number theory. It can also be used to prepare for mathematical Olympiads. Elementary algebra, arithmetic and some calculus knowledge are the only prerequisites. Number theory gives precise proofs and theorems of an irreproachable rigor and sharpens analytical thinking, which makes this book perfect for anyone looking to build their mathematical confidence.
Author: Florentin Smarandache
Author: Florentin Smarandache
Author: FLORENTIN SMARANDACHE 
Author: Florentin Smarandache 
Author: Florentin Smarandache 
Author: Florentin Smarandache
Author: FLORENTIN SMARANDACHE 
Author: Florentin Smarandache
Author: Florentin Smarandache
Author: Oscar Levin
Author: Ellina Grigorieva