Diofantske jednadžbe višeg stupnja

master's thesis

• Author: Dora Sučić
• Mentor: Zrinka Franušić (mentor)
• Committee member: Zrinka Franušić (predsjednik povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Committee member: Željka Milin Šipuš (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Diofantska jednadžba je jednadžba oblika \[f(x_1, x_2, \ldots, x_n)=0,\] gdje je \(f\) polinom s cjelobrojnim koeficijentima, te za koju tražimo samo cjelobrojna rješenja. U ovom diplomskom radu prikazujemo neke metode rješavanja diofantskih jednadžbi kao što su metoda faktorizacije, metoda matematičke indukcije, te parametarska metoda. Također, prezentiramo neke napredne metode koje uključuju Gaussove cijele brojeve i kvadratna polja. Jedno poglavlje posvećeno je nekim klasičnim diofantskim jednadžbama kao što su Pitagorina i Pellova jednadžba.

Abstract (english)

A diophantine equation is an equation of the form \[f(x_1, x_2, \ldots, x_n)=0,\] where \(f\) is a polynomial with integral coefficients and such that only integer solutions are sought. In this diploma thesis, we present some methods in solving Diophantine equations such as decomposition method, parametric method, method of mathematical induction. Also, we introduce some advanced methods involving Gaussian integers and quadratic fields. One chapter is devoted to some classical Diophantine equations like Pythagorean-type equations and Pell’s equation.

• Keywords: diofantska jednadžba; metode rješavanja diofanstkih jednadžbi; Pitagorina jednadžba; Pellova jednadžba
• Keywords (english): diophantine equation; methods in solving Diophantine equations; Pythagorean-type equations; Pell’s equation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:612452
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-06-17 12:00:08