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undergraduate thesis
Rješavanje kongruencija
2018. urn:nbn:hr:126:437823
Pejić, Ana Maria
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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Pejić, A. M. (2018). Rješavanje kongruencija (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:437823

Pejić, Ana Maria. "Rješavanje kongruencija." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:437823

Pejić, Ana Maria. "Rješavanje kongruencija." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:437823

Pejić, A. M. (2018). 'Rješavanje kongruencija', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 30 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:437823

Pejić AM. Rješavanje kongruencija [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2024 December 30] Available at: https://urn.nsk.hr/urn:nbn:hr:126:437823

A. M. Pejić, "Rješavanje kongruencija", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:126:437823

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Metadata
TitleRješavanje kongruencija
Title (english)Solving congruences
AuthorAna Maria Pejić
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 country2018-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U ovom završnom radu upoznat ćemo se s načinima i metodama rješavanja različitih tipova kongruencija. Na početku ćemo definirati sustave ostataka koji su nam vrlo bitni pri određivanju rješenja kongruencija. Nadalje, prikazat ćemo postupak rješavanja linearnih kongruencija, polinomijalnih kongruencija sa složenim modulima te polinomijalnih kongruencija s prostim potenciranim modulima. Navest ćemo te na primjerima primjenjivati Kineski teorem o ostatcima koji nam je koristan pri rješavanju sustava linearnih kongruencija. Također ćemo navesti i kroz primjere prikazati primjenu Fermatovog i Lagrangeovog teorema koji su nam korisni pri rješavanju kongruencija s prostim modulima.
Abstract (english)
In this final paper we will introduce ways and methods of solving different types of congruences. At the beginning we will define the residue systems, which are very important in obtaining solutions of congruences. Furthermore, the procedure of solving linear congruences, polynomial congruences with composite moduli and polynomial congruences with prime power moduli will be shown. We will cite The Chinese remainder theorem, which is very useful in solving simultaneous linear congruences, and apply it to examples. We will also cite and through examples present the applications of Fermat’s and Lagrange’s theorem, which are useful in solving congruences with prime moduli.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:437823
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
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Created on2018-10-18 07:52:42