Abstract

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]} and thus, examining all equations of the form p(x) = s(x)a(x)+t(x)b(x).

Keywords:

Algebra, algebraic properties, cryptography, division property, Euclidean algorithm, greatest common divisor, trading,

References

Competing interests

The authors have no competing interests.

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Copyright

The authors have no competing interests.