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master's thesis
Fermatova četvorka
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:359463
Čupić, Lovro
University of Zagreb
Faculty of Science
Department of Mathematics
University of Zagreb
Faculty of Science
Department of Physics

Institutional repository: Repository of the Faculty of Science

Cite this document

Čupić, L. (2020). Fermatova četvorka (Master's thesis). Zagreb: University of Zagreb, Faculty of Science; Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:359463

Čupić, Lovro. "Fermatova četvorka." Master's thesis, University of Zagreb, Faculty of Science; University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:359463

Čupić, Lovro. "Fermatova četvorka." Master's thesis, University of Zagreb, Faculty of Science; University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:359463

Čupić, L. (2020). 'Fermatova četvorka', Master's thesis, University of Zagreb, Faculty of Science; University of Zagreb, Faculty of Science, accessed 03 January 2025, https://urn.nsk.hr/urn:nbn:hr:217:359463

Čupić L. Fermatova četvorka [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2025 January 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:359463

L. Čupić, "Fermatova četvorka", Master's thesis, University of Zagreb, Faculty of Science, Zagreb; University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:359463

Metadata
TitleFermatova četvorka
AuthorLovro Čupić
MentorZrinka Franušić (mentor)
Committee memberZrinka Franušić (predsjednik povjerenstva)
Committee memberTomislav Pejković (član povjerenstva)
Committee memberMaja Planinić (član povjerenstva)
Committee memberFilip Najman (član povjerenstva)
Committee memberTihomir Vukelja (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
GranterUniversity of Zagreb
Faculty of Science
(Department of Physics)
Zagreb
Defense date and country2020-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Fermatova četvorka je skup \(\{1,3,8,120 \}\) sa svojstvom da je umnožak bilo koja dva njegova elementa uvećan za 1 potpuni kvadrat. Općenito, skupovi od \(m\) prirodnih brojeva s danim svojstvom nazivaju se Diofantove \(m\)-torke. U ovom radu pokazujemo da ako je \(\{1,3,8, d \}\) Diofantova četvorka, tada je \(d = 120\). To su izvorno dokazali Baker i Davenport u [1], gdje su uveli metodu osnovanu na teoriji linearnih formi u logaritmima algebarskih brojeva i metodu redukcije temeljenu na verižnim razlomcima.
Abstract (english)
Fermat’s quadruple is a set \(\{1,3,8,120 \}\) with a property that the product of any two of its elements increased by 1 is a perfect square. Generally, sets of \(m\) positive integers with the given property are called Diophantine \(m\)-tuples. In this thesis, we show that if \(\{1,3,8, d \}\) is a Diophantine quadruple, then \(d = 120\). This was originally proved by Baker and Davenport in [1], where they introduced a method based on the theory of linear forms in the logarithms of algebraic numbers and a reduction method based on continued fractions.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:359463
Study programmeTitle: Mathematics and Physics Education; specializations in: Mathematics and Physics Education
Course: Mathematics and Physics Education
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije matematike i fizike (magistar/magistra edukacije matematike i fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-03-04 13:04:50