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Article Information:
On Some Algebraic Properties of the Euclidean Algorithm with Applications to Real Life
E.A. Alhassan, K.N. Simon, J.M. Bunyan and A. Gregory
Corresponding Author: E.A. Alhassan
Submitted: May 04, 2014
Accepted: June 08, 2014
Published: November 25, 2014 |
Abstract:
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The study analyzed the algebraic properties of the Euclidean algorithm in details. The analysis included a detailed step by step approach in understanding the algorithm, the extended form of the algorithm, computation of the Greatest Common Divisor (GCD) and its algebraic properties and their applications in algebra and cryptography. We also showed how the Euclidean algorithm could be applied to trading for the maximization of returns. In our approach, we assumed that gcd[a(x); b(x)] is the monic polynomial of minimal degree within the set G = {s(x)a(x)+t(x)b(x): s(x), t(x) ∈ F[x]}
Key words: Algebra, algebraic properties, cryptography, division property, Euclidean algorithm, greatest common divisor, trading
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Cite this Reference:
E.A. Alhassan, K.N. Simon, J.M. Bunyan and A. Gregory, . On Some Algebraic Properties of the Euclidean Algorithm with Applications to Real Life. Research Journal of Mathematics and Statistics, (4): 46-52.
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ISSN (Online): 2040-7505
ISSN (Print): 2042-2024 |
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