Metode rješavanja Pellove jednadžbe

master's thesis

• Author: Jasna Bagović
• Mentor: Alan Filipin (mentor)
• Committee member: Alan Filipin (predsjednik povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Josip Tambača (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu, glavnu ulogu je imao Pell, odnosno njegove jednadžbe. Cilj rada je bio definirati i dati efikasne načine rješavanja Pellovih jednadžbi. Na samom početku rada su navedeni neki važniji rezultati koji se tiču diofantskih jednadžbi jer je Pellova jednadžba zapravo specijalan slučaj diofantske jednadžbe. Nadalje, dane su definicije Pellove i pellovske jednadžbe, kao i teoremi koji daju nužne i dovoljne uvjete za egzistenciju i strukturu tih rješenja. Kroz drugo poglavlje su opisane metode kojima se određuju rješenja tih jednadžbi, dok je u trećem poglavlju opisan takozvani Arhimedov problem stoke, te je dana veza tog problema s Pellovim jednadžbama.

Abstract (english)

In this thesis, the main role had Pell, in fact his equations. The aim of the study was to define and provide efficient ways of solving Pell’s equations. At the very beginning of this thesis are some important results concerning Diophantine equations because Pell’s equation is a special case of Diophantine equation. Further, there are also definitions of Pell’s and generalized Pell equations as well as theorems which are giving necessary and sufficient conditions for existence and structure of such solutions. The second chapter describes methods for determining solutions of these equations, while the third chapter describes the so-called Archimedes’ cattle problem and finds connection between that problem and Pell’s equation.

• Keywords: Pellova jednadžba; diofantska jednadžba; pellovska jednadžba; Arhimedov problem stoke
• Keywords (english): Pell’s equation; Diophantine equations; generalized Pell equations; Archimedes’ cattle problem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:048822
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-05-09 11:09:04