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master's thesis
Kvadratni ostatci
2024. urn:nbn:hr:126:399897
Lamot, Lorena
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Lamot, L. (2024). Kvadratni ostatci (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:399897

Lamot, Lorena. "Kvadratni ostatci." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:399897

Lamot, Lorena. "Kvadratni ostatci." Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:399897

Lamot, L. (2024). 'Kvadratni ostatci', Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:399897

Lamot L. Kvadratni ostatci [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:126:399897

L. Lamot, "Kvadratni ostatci", Master's thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:399897

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Metadata
TitleKvadratni ostatci
Title (english)Quadratic Residues
AuthorLorena Lamot
MentorMirela Jukić Bokun (mentor)
Committee memberTomislav Marošević (predsjednik povjerenstva)
Committee memberMirela Jukić Bokun (član povjerenstva)
Committee memberIvan Soldo (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-10-17, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U ovom radu definirani su kvadratni ostatci i navedene neke korisne tvrdnje vezane uz njih. Uveden je pojam Legendreovog simbola te su pokazana njegova osnovna svojstva i primjene. Iskazan je i dokazan Gaussov kvadratni zakon reciprociteta te je pokazana njegova primjena u Pepinovom testu prostosti. Definiran je Jacobijev simbol i pokazana su njegova osnovna svojstva. Naveden je algoritam za izračunavanje Jacobijevog simbola te je dokazano da i za njega vrijedi Zakon kvadratnog reciprociteta. Na kraju su definirani Eulerovi pseudoprosti brojevi te su iskazani i dokazani rezultati koji se koriste u testovima prostosti.
Abstract (english)
In this paper, quadratic residues are defined and some useful statements related to them are presented. The concept of the Legendre symbol is introduced, along with its basic properties and applications. Gauss’s quadratic reciprocity law is stated and its application in Pepin’s primality test is demonstrated. The Jacobi symbol is defined and its basic properties are shown. An algorithm for calculating the Jacobi symbol is provided and it is proven that the Law of Quadratic Reciprocity also applies to it. Finally, Euler’s pseudoprimes are defined and results used in primality tests are stated and proven.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:399897
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-10-25 10:22:23