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master's thesis
Kongruencije višeg reda
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. urn:nbn:hr:126:694694
Lalić, Jelena
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

Institutional repository: Repository of School of Applied Mathematics and Informatics

Cite this document

Lalić, J. (2016). Kongruencije višeg reda (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:694694

Lalić, Jelena. "Kongruencije višeg reda." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:694694

Lalić, Jelena. "Kongruencije višeg reda." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:694694

Lalić, J. (2016). 'Kongruencije višeg reda', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:694694

Lalić J. Kongruencije višeg reda [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:126:694694

J. Lalić, "Kongruencije višeg reda", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:126:694694

Metadata
TitleKongruencije višeg reda
Title (english)High order congruences
AuthorJelena Lalić
MentorIvan Matić (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 country2016-12, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U ovom radu upoznat ćemo se s metodama određivanja uvijeta za egzistenciju rješenja polinomijalnih kongruencija te pronalaženja istih. Glavni dio rada podijeljen je u pet poglavlja,od kojih prva dva daju dovoljno temeljnog znanja o djeljivosti i kongruencijama te njihovim svojstvima. Također su promatrane linearne kongruencije kao i rješavanje sustava linearnih kongruencija koristeći Kineski teorem o ostacima. U četvrtom poglavlju posebna paznjaje usmjerena na kvadratne kongruencije. Definiran je pojam Legendreovog simbola te supredstavljeni rezultati koji vode lakšem određivanju njegove vrijednosti. Svi teorijski rezultatiu radu primjenjeni su na konkretnim primjerima. U posljednjem poglavlju ćemo preko definicije reda prirodnog broja a modulo n doći do pojma primitivnog korijena modulo n.Pokazat ćemo kako odrediti je li neki prirodni broj primitivan korijen modulo n. Spomenuti pojam bit ce ključan u rješavanju polinomijalnih kongruencija.
Abstract (english)
In this paper we will introduce the methods of determining the conditions for the existence ofsolutions of polynomial congruence and technique to obtain such solutions. The main part ofthis paper is divided into five chapters, of which the first two provide enough basic knowledgeabout the divisibility and congruence and their properties. We study a linear congruence andsolving systems of linear congruences using the Chinese theorem of residues. In the fourthchapter, special attention is focused on quadratic congruence. We define Legendre symboland presents the results which lead to easier determine its value. All theoretical results inthe work were applied to particular examples. In the last chapter we introduce the conceptof the order of integer modulo n and then we define primitive roots modulo n and show howto determine whether an integer is primitive modulo n or not. The mentioned term will bea key to solving polynomial congruence.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:694694
Study programmeTitle: Mathematics and Computer Science
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2017-01-09 08:17:12