Razlomački skupovi

master's thesis

• Author: Renata Crevar
• Mentor: Tomislav Pejković (mentor)
• Committee member: Tomislav Pejković (predsjednik povjerenstva)
• Committee member: Vedran Krčadinac (član povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Committee member: Robert Manger (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-07-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Razlomački skup je skup kojeg dobivamo kada uzmemo kvocijent svakog para elemenata danog podskupa skupa prirodnih brojeva. Neka je \(A \subseteq \mathbb{N}\) podskup skupa prirodnih brojeva. Tada je \(R(A)=\{a / b: a, b \in A\}\) njemu pridruženi razlomački skup. Ovaj diplomski rad sadrži tri poglavlja. U prvom poglavlju izlažemo osnovne pojmove i rezultate iz teorije brojeva koji se koriste u nastavku rada. U drugom poglavlju iskazujemo i dokazujemo četiri zanimljiva teorema o razlomačkim skupovima u realnim brojevima. U zadnjem poglavlju ovog rada promatramo razlomačke skupove u \(p\)-adskim brojevima, gdje je \(p\) neki prost broj.

Abstract (english)

A quotient set is the set we get when we take the quotient of each pair of the elements of a given subset of a set of positive integers. Let \(A \subseteq \mathbb{N}\) be a subset of the set of positive integers. Then \(R(A)=\{a / b: a, b \in A\}\) denotes the corresponding quotient set. This graduate thesis is divided into three chapters. In the first chapter we give some of the fundamental terms and results from the theory of numbers used throughout the rest of the thesis. In the second chapter we state and prove four interesting theorems about quotient sets in real numbers. In the last chapter of this thesis, we study quotient sets in \(p\)-adic numbers, where \(p\) is some prime number.

• Keywords: razlomački skup; teorija brojeva
• Keywords (english): quotient set; number theory
• Language: croatian
• URN:NBN: urn:nbn:hr:217:538998
• 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: 2020-12-22 11:57:13