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undergraduate thesis
Euklidov algoritam i primjene
2020. urn:nbn:hr:126:041306
Rengel, Maja
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

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Rengel, M. (2020). Euklidov algoritam i primjene (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:041306

Rengel, Maja. "Euklidov algoritam i primjene." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:041306

Rengel, Maja. "Euklidov algoritam i primjene." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:041306

Rengel, M. (2020). 'Euklidov algoritam i primjene', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 05 February 2025, https://urn.nsk.hr/urn:nbn:hr:126:041306

Rengel M. Euklidov algoritam i primjene [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2025 February 05] Available at: https://urn.nsk.hr/urn:nbn:hr:126:041306

M. Rengel, "Euklidov algoritam i primjene", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:041306

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Metadata
TitleEuklidov algoritam i primjene
Title (english)The Euclidean Algorithm and its Applications
AuthorMaja Rengel
MentorIvan Soldo (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Algebra, Analysis and Number Theory Research Group)
Osijek
Defense date and country2020-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U ovom završnom radu bavit ćemo se promatranjem Euklidova algoritma i nekih njegovih primjena. Najprije ćemo uvesti pojmove i neke važne tvrdnje vezane uz djeljivost, doći do algoritma te pokazati primjenu na traženje najvećeg zajedničkog djelitelja danih brojeva. Nakon toga ćemo promatrati primjenu algoritma na još neke strukture. U prvom ćemo se poglavlju baviti detaljnijim proučavanjem najvećih zajedničkih djelitelja dvaju brojeva nakon čega slijedi uvođenje Euklidova algoritma i primjena na iste. Nadalje ćemo uvesti pojam linearnih diferencijalnih jednadžbi, proširiti algoritam i pokazati njegovu primjenu na rješavanje istih. Naposlijetku, proučavat ćemo razvoj realnih brojeva u jednostavne verižne razlomke uz pomoć Euklidova algoritma te ćemo pokazati još jedan način rješavanja linearnih diofantskih jednadžbi pomoću Euklidova algoritma.
Abstract (english)
In this final paper, we will focus to the Euclidean algorithm and its applications. Firstly, we will introduce definitions and some important claims connected to divisibility, come to the algorithm, and show how to apply it to find the largest common divisor of a given number. After that, we will observe an application of the algorithm to few other structures. In the first chapter, we will observe the largest common divisor of two numbers and follow it with the introduction of the Euclidean algorithm and its applications. Furthermore, we will introduce the linear diophantine equations, expand the algorithm and show how to apply it in their solving. Finally, we will consider numbers in the form of the simple continued fractions expression by using the Euclidean algorithm. Moreover, we will show one more method of solving linear diophantine equations with the help of the Euclidean algorithm.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:041306
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-10-27 11:31:43