Od Pitagorine do Fermatove jednadžbe

master's thesis

• Title (english): From Pythagoras to Fermat's equation
• Author: Jelena Župarić-Iljić
• Mentor: Andrej Dujella (mentor)
• Committee member: Andrej Dujella (predsjednik povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Goranka Nogo (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Teorija brojeva, grana matematike koja proučava svojstva i međusobne odnose različitih vrsta brojeva, na prvu možda odaje dojam jedne od najjednostavnijih grana matematike. Međutim, ona sadrži mnoštvo jednostavno oblikovanih, ali teško dokazivih problema, od kojih neki ostaju nerazriješeni čak i stoljećima nakon svog izricanja. Posljednji Fermatov teorem primjer je ovakvog problema i glavna tema rada. Iako nema jednostavne primjene u znanosti, njegova važnost leži u tome što su pokušaji dokazivanja ovog, naizgled nerješivog problema doveli do razvoja nekih od najvažnijih grana moderne matematike. Također, njegov je dokaz ujedinio mnoštvo nadarenih matematičara i objedinio cijelu širinu matematike, čak i objekte koji su djelovali nepomirljivima. Svrha ovog rada je predstaviti povijesno-matematički tijek konstruiranja i dokazivanja Posljednjeg Fermatovog teorema, počevši od njegovih korijena u vidu Pitagorina teorema. Pitagorin teorem, čije se verzije javljaju u drevnim babilonskim, kineskim i indijskim zapisima, usko je vezan za Pitagorine trojke, koje se takoder obrađuju u ovom radu. Posljednji se dio bavi razmatranjem Posljednjeg Fermatovog teorema u prstenu polinoma s kompleksnim koeficijentima.

Abstract (english)

Number theory which is a branch of mathematics that studies the properties and relationships of different types of numbers, at first may seem like one of the simplest branches of mathematics. However, it contains a multitude of simply formulated yet problems that are difficult to prove, and some of them remain unsolved centuries after their formulation. Fermat’s Last theorem is an example of this kind of problem and also the main topic of this thesis. Although it has no straightforward application in science, its importance lies in attempts to prove this seemingly unsolvable problem which has led to the development of some of the most important branches of modern mathematics. Nevertheless, its proof has united a multitude of gifted mathematicians and unified the entire breadth of mathematics, including objects that seemed irreconcilable. The purpose of this thesis is to present the genealogical historical-mathematical process of constructing and proving Fermat’s Last Theorem, starting from its roots in the form of the Pythagorean theorem. The Pythagorean theorem, versions of which already had appeared in ancient Babylonian, Chinese and Indian records, is closely related to the Pythagorean triples, which are also discussed in this thesis. The last part analyzes Fermat’s Last Theorem over the ring of polynomials with complex coefficients.

• Keywords: teorija brojeva; Posljednji Fermatov teorem; Pitagorin teorem; Pitagorine trojke; prsten polinoma
• Keywords (english): number theory; Fermat’s Last theorem; Pythagorean theorem; Pythagorean triples; ring of polynomials
• Language: croatian
• URN:NBN: urn:nbn:hr:217:377563
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-11-11 10:57:14