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undergraduate thesis
Kvadratni zakon reciprociteta
2021. urn:nbn:hr:126:260296
Mink, Katarina
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Mink, K. (2021). Kvadratni zakon reciprociteta (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:260296

Mink, Katarina. "Kvadratni zakon reciprociteta." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:260296

Mink, Katarina. "Kvadratni zakon reciprociteta." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:260296

Mink, K. (2021). 'Kvadratni zakon reciprociteta', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 12 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:260296

Mink K. Kvadratni zakon reciprociteta [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2024 November 12] Available at: https://urn.nsk.hr/urn:nbn:hr:126:260296

K. Mink, "Kvadratni zakon reciprociteta", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:260296

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Metadata
TitleKvadratni zakon reciprociteta
Title (english)Quadratic Reciprocity Law
AuthorKatarina Mink
MentorMirela Jukić Bokun (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2021-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Algebra
Abstract
U ovom radu proučavamo kvadratni zakon reciprociteta. Prvo se upoznajemo s pojmovima koji će nam trebati, kao što su kongruencije, kvadratni ostatci i Legendreov simbol. Zatim iskazujemo kvadratni zakon reciprociteta i dokazujemo ga na dva načina, pomoću Gaussove leme i na temelju množenja elemenata koji imaju određena svojstva. Na kraju proučavamo primjene kvadratnog zakona reciprociteta u dokazivanju tvrdnji o prostim brojevima i u Fermatovom teoremu o sumi dva kvadrata.
Abstract (english)
In this paper we study quadratic reciprocity law. First we introduce terms we will need, such as congruences, square residues and the Legendre symbol. Then we express the quadratic reciprocity law and prove it in two ways, using the Gaussian lemma and using the multiplication of elements with specific properties. Finally, we study the applications of the quadratic reciprocity law in proving claims about prime numbers and in Fermat’s two square theorem.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:260296
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 on2021-10-05 10:11:52