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master's thesis
Pellova jednadžba
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2023. urn:nbn:hr:126:617315
Balog, Karla
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

Institutional repository: Repository of School of Applied Mathematics and Informatics

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Balog, K. (2023). Pellova jednadžba (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:617315

Balog, Karla. "Pellova jednadžba." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:617315

Balog, Karla. "Pellova jednadžba." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2023. https://urn.nsk.hr/urn:nbn:hr:126:617315

Balog, K. (2023). 'Pellova jednadžba', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 17 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:617315

Balog K. Pellova jednadžba [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2023 [cited 2024 November 17] Available at: https://urn.nsk.hr/urn:nbn:hr:126:617315

K. Balog, "Pellova jednadžba", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:126:617315

Metadata
TitlePellova jednadžba
Title (english)Pell's Equation
AuthorKarla Balog
MentorIvan Soldo (mentor)
Committee memberMirela Jukić Bokun (predsjednik povjerenstva)
Committee memberIvan Soldo (član povjerenstva)
Committee memberTomislav Marošević (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2023-06-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U ovom diplomskom radu najprije smo naveli definicije te neke općenite rezultate vezane uz neke oblike diofantskih jednadžbi, a zatim se u ostatku rada usmjerili na specijalan oblik nelinearne diofantske jednadžbe: Pellovu jednadžbu. Osim toga, proučili smo pelovske jednadžbe \(x^{2}-dy^{2}=\pm 1,\pm 4\) . Naveli smo dokaze o nužnim i dovoljnim uvjetima postojanja njihovih rješenja, pokazali strukturu rješenja te naposlijetku pokazali kako te jednadžbe riješiti korištenjem verižnih razlomaka i drevne indijske Chakravala metode.
Abstract (english)
In this final paper, we first stated the definitions and some general results related to some types of Diophantine equations. After that, we focused on a special type of nonlinear Diophantine equation: Pell’s equation. Additionally, we studied the equations \(x^{2}-dy^{2}=\pm 1,\pm 4\). We presented the necessary and sufficient conditions for the existence of their solutions, showed the structure of the solutions and finally showed how to solve these equations using the continued fractions method and the ancient Indian Chakravala method.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:617315
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 on2023-06-02 11:09:35