Gaussovi cijeli brojevi

master's thesis

• Title (english): Gaussian integers
• Author: Martina Novotny
• Mentor: Zrinka Franušić (mentor)
• Committee member: Zrinka Franušić (predsjednik povjerenstva)
• Committee member: Željko Skoko (član povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Committee member: Darko Androić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-07-21, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Skup Gaussovih cijelih brojeva označavamo sa \(\mathbb{Z}[i]=\{a+bi:a,b\in\}\) i on čini komutativni prsten s jedinicom s obzirom na zbrajanje i množenje kompleksnih brojeva. U radu se obrađuju standardne teme kao što su djeljivost, Gaussovi prosti brojevi, veza sa sumama kvadrata, Euklidov algoritam, jedinstvena faktorizacija, itd. Poseban je naglasak na vizualnim iterpretacijama i ilustracijama koje su izvedene pomoću \({GeoGebre}\).

Abstract (english)

The set of Gaussian integers is denoted by \(\mathbb{Z}[i]=\{a+bi:a,b\in\}\) and it forms a commutative ring with the unit in regard to addition and multiplication of complex numbers. The thesis deals with standard topics such as divisibility, Gaussian prime numbers, connection to the sums of squares, Euclid's algorithm, unique factorization, etc. There is a special emphasis on the visual interpretations and illustrations that were performed using \({GeoGebra}\).

• Keywords: kompleksni brojevi; djeljivost; Gaussovi prosti brojevi; sume kvadrata; Euklidov algoritam; jedinstvena faktorizacija
• Keywords (english): complex numbers; divisibility; Gauss prime numbers; sums of squares; Euclid's algorithm; unique factorization
• Language: croatian
• URN:NBN: urn:nbn:hr:217:493442
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-09-16 11:40:41