O nekim Eulerovim doprinosima u teoriji brojeva

master's thesis

• Author: Jelena Cafuk
• Mentor: Zrinka Franušić (mentor)
• Committee member: Zrinka Franušić (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Luka Grubišić (član povjerenstva)
• Committee member: Goran Radunović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Leonhard Euler (1707.-1783.) najproduktivniji je matematičar svih vremena. Dao je ogroman doprinos svakom matematičkom području svog vremena, ali i mnogim drugim znanostima kao što su geografija, fizika, teorija glazbe, ... Postavio je temelje nekim matematičkim granama, a smatra se da je posebnu "virtuoznost'' pokazao baveći se teorijom brojeva. U radu ćemo opisati samo neke njegove doprinose elementarnoj teoriji brojeva, primjerice dokaz Malog Fermatovog teorema, Velikog Fermatovog teorema za \(n=3\) i Teorema o dva kvadrata te mnoge zaključke vezane uz djeljivost prirodnih brojeva, Legendreov simbol i Pellovu jednadžbu.

Abstract (english)

Leonhard Euler (1707. - 1783.) is the most productive mathematician of all time. He made enormous contributions to every mathematical branch of his time as well as to many other fields of science such as geography, physics, music theory,… He laid the foundations for some mathematical branches, however, number theory is considered the branch where his “virtuosity” was most evident. This paper describes just some of his contributions to elementary number theory, such as the proof of Fermat’s little theorem, Fermat’s last theorem for \(n = 3\) and his Theorem on the sum of two squares as well as many conclusions related to the divisibility of natural numbers, the Legendre symbol and Pell’s equation.

• Keywords: Euler; teorija brojeva; Mali Fermatov teorem; Veliki Fermatov teorem; Teorem o dva kvadrata; Legendreov simbol; Pellova jednadžba
• Keywords (english): Euler; number theory; Fermat’s little theorem; Fermat’s last theorem; Theorem on the sum of two squares; Legendre symbol; Pell’s equation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:863766
• 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: 2019-03-05 11:43:58