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master's thesis
Fermatov doprinos u teoriji brojeva
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:946216
Plantak, Valentina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Plantak, V. (2018). Fermatov doprinos u teoriji brojeva (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:946216

Plantak, Valentina. "Fermatov doprinos u teoriji brojeva." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:946216

Plantak, Valentina. "Fermatov doprinos u teoriji brojeva." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:946216

Plantak, V. (2018). 'Fermatov doprinos u teoriji brojeva', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:946216

Plantak V. Fermatov doprinos u teoriji brojeva [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:946216

V. Plantak, "Fermatov doprinos u teoriji brojeva", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:946216

Metadata
TitleFermatov doprinos u teoriji brojeva
AuthorValentina Plantak
MentorZrinka Franušić (mentor)
Committee memberGoran Radunović (predsjednik povjerenstva)
Committee memberZrinka Franušić (član povjerenstva)
Committee memberMaja Resman (član povjerenstva)
Committee memberPavle Goldstein (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Pierre de Fermat jedan je od najvećih matematičara 17. stoljeća. Smatra ga se utemeljiteljem moderne teorije brojava. Glavni cilj ovog diplomskog rada je prikazati i dijelom dokazati Fermatove rezultate i doprinose u teoriji brojeva. Fermat je dao čitav niz tvrdnji, uglavnom bez dokaza, koje su se godinama, a neke i stoljećima kasnije pokazale istinitima. Fermat je poznat po brojevima oblika \(F_m=2^{2^{m}}+1, m \in \mathbb{N}\) koji se zovu Fermatovi brojevi te po svom doprinosu u razvoju diofantskih jednadžbi. U radu su iskazani i dokazani (svi osim posljednjeg) Fermatovi teoremi: Mali Fermatov teorem, Teorem o zbroju dva kvadrata, Teorem o poligonalnim brojevima i Veliki Fermatov teorem. Osim teorema u radu su opisane i na primjerima objašnjene dvije Fermatove metode: Fermatova metoda faktorizacije i Fermatova metoda neprekidnih silazaka.
Abstract (english)
Pierre de Fermat is one of the greatest mathematicians of 17. century. He is considered a founder of modern number theory. The main purpose of this work is to present and partly to prove the results and contributions Fermat’s contributions to number theory. Fermat gave a whole series of assertions, mostly without the proof, which have been years, and some of them centuries later proved to be true. Fermat is famous for his numbers \(F_m=2^{2^{m}}+1, m \in \mathbb{N}\), which we call Fermat’s numbers, and for his contributions in development of Diophant’s equations. In the work are presented and proved (all except the last one) following theorems: Fermat’s Little theorem, Two-Square Theorem, Fermat polygonal number theorem and Fermat’s Last Theorem. Except the theorems, two Fermat’s methods: Fermat’s factorizations method and Fermat’s method of infinite descent are described and explained trough the examples.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:946216
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-06-10 12:16:01