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Osječki matematički list, Vol. 13 No. 2, 2013.

Professional paper

Applications of the Euclidean algorithm

Mateja Đumić orcid id orcid.org/0000-0001-8980-6315 ; Odjel za matematiku, Sveučilište J.J.Strossmayera u Osijeku, Osijek, Hrvatska
Mirela Jukić Bokun orcid id orcid.org/0000-0003-3461-8506 ; Odjel za matematiku, Sveučilište J.J.Strossmayera u Osijeku, Osijek, Hrvatska

Full text: croatian pdf 279 Kb

page 121-137

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Abstract

In this article, we show how the Euclidean algorithm can be used for solving linear Diophantine equations and we apply the obtained results to various types of tasks. We also show that the Euclidean algorithm and expansion of a rational number to a continued fraction are closely related and we discuss some properties of those expansions.

Keywords

divisibility; Euclidean algorithm; Diophantine equation; continued fraction

Hrčak ID:

114024

URI

https://hrcak.srce.hr/114024

Publication date:

18.12.2013.

Article data in other languages: croatian

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