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undergraduate thesis
Kvadratni ostatci i primjene
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. urn:nbn:hr:126:107101
Rezo, Ana
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group

Cite this document

Rezo, A. (2020). Kvadratni ostatci i primjene (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:107101

Rezo, Ana. "Kvadratni ostatci i primjene." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:107101

Rezo, Ana. "Kvadratni ostatci i primjene." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:107101

Rezo, A. (2020). 'Kvadratni ostatci i primjene', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 28 March 2023, https://urn.nsk.hr/urn:nbn:hr:126:107101

Rezo A. Kvadratni ostatci i primjene [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2023 March 28] Available at: https://urn.nsk.hr/urn:nbn:hr:126:107101

A. Rezo, "Kvadratni ostatci i primjene", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:107101

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Metadata
TitleKvadratni ostatci i primjene
Title (english)Quadratic Residues and Its Applications
AuthorAna Rezo
MentorIvan Soldo (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Algebra and Calculus Research Group)
Osijek
Defense date and country2020-09-10, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U ovom završnom radu upoznat ćemo se s kvadratnim ostatcima i nekim njihovim primjenama. U uvodu ćemo definirati kvadratne ostatke i navest ćemo neke primjere. U prvom poglavlju definirat ćemo Legendreov simbol i navest ćemo osnovna svojstva Legendreova simbola koja ćemo primijeniti na primjeru. Upoznat ćemo se i s Eulerovim teoremom. U drugom poglavlju iskazat ćemo i dokazati Gaussovu lemu i kvadratni zakon reciprociteta te ćemo vidjeti primjenu kvadratnog zakona reciprociteta. U trećem poglavlju definirat ćemo Jacobijev simbol te ćemo se susresti sa svojstvima Jacobijeva simbola koja ćemo iskoristiti u primjeru. U posljednjem poglavlju iskazat ćemo i dokazati nekoliko primjena kvadratnih ostataka na rješavanje diofantskih jednadžbi.
Abstract (english)
In this final paper we are going to introduce ourselves to quadratic residues and some of its applications. At the beginning, we will define quadratic residues and give some examples. In the first chapter, we will define Legendre’s symbol, enlist the basic properties of Legendre’s symbol and use those properties on an example. We will be, as well, introduced to Euler’s theorem. In the second chapter, we are going to express and prove Gauss’s lemma, quadratic law of reciprocity and we will show the usage of quadratic law of reciprocity. In the third chapter, we will define and introduce ourselves to the properties of Jacobi symbol and we’ll show the usage of the properties on an example. In the last chapter, we are going to express and prove some of applications of quadratic residues on Diophantine equations.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:107101
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
RepositoryRepository of Department of Mathematics Osijek
Created on2020-09-21 07:09:17