Teorija brojeva u zadatcima s natjecanja

master's thesis

• Author: Kristina Logarušić
• Mentor: Zrinka Franušić (mentor)
• Committee member: Zrinka Franušić (predsjednik povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Committee member: Maja Starčević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-07-18, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Teorija brojeva jedna je od najstarijih i najljepših grana matematike. Budući da mnogi problemi u teoriji brojeva ne zahtijevaju veliko znanje i imaju puno varijacija, često se pojavljuju u matematičkim natjecanjima. Proučavajući zadatke s raznih domaćih, međunarodnih i inozemnih matematičkih natjecanja, u ovom radu prikazali smo zadatke s natjecanja i njihova rješenja vezane za djeljivost, proste brojeve i faktorizaciju, kongruencije te diofantske jednadžbe.

Abstract (english)

Number Theory is one of the oldest and one most beautiful branches of Mathematics. Since many problems in this branch use little knowledge and have many variations, they frequently occur in mathematical competitions. Studying assignments from various domestic, overseas and international math competitions, in this thesis we have included mathematics contest problems and their solutions related to divisibility, prime numbers and factorization, congruences and Diophantine equations.

• Keywords: teorija brojeva; matematička natjecanja; djeljivost; prosti brojevi; faktorizacija; kongruencije; diofantske jednadžbe
• Keywords (english): number theory; mathematical competitions; divisibility; prime numbers; factorization; congruences; Diophantine equations.
• Language: croatian
• URN:NBN: urn:nbn:hr:217:851956
• 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: 2018-02-02 12:28:12