diplomsko delo
Tamara Murko (Author), Daniel Eremita (Mentor)

Abstract

V diplomskem delu so uvodoma predstavljene osnove teorije aritmetičnih funkcij. Naslednje poglavje je namenjeno popolnim številom in Mersennovim praštevilom. Obravnavana je tudi domneva abc. Ob predpostavki, da je domneva abc resnična, je izpeljan asimptotični Fermatov izrek, asimptotična Catalanova domneva, dokazan je obstoj neskončno mnogo Wieferichovih praštevil. Osrednja tema diplomskega dela je radikal popolnega števila. V zadnjem poglavju je izpeljanih nekaj rezultatov, povezanih z razdaljo med popolnima številoma, ki nastanejo kot posledica domneve abc.

Keywords

aritmetične funkcije;Mersennova praštevila;praštevila;popolna števila;domneva abc;radikal;diplomska dela;

Data

Language: Slovenian
Year of publishing:
Source: Maribor
Typology: 2.11 - Undergraduate Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [T. Murko]
UDC: 511.174(043.2)
COBISS: 19313928 Link will open in a new window
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Downloads: 154
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Other data

Secondary language: English
Secondary title: THE DISTANCE BETWEEN PERFECT NUMBERS AND ABC CONJECTURE
Secondary abstract: The graduation thesis initially presents the theory of arithmetic function. The following chapter regards to perfect numbers and Mersenne primes. We consider the abc conjecture. On the assumption that the abc conjecture is true, we derive asymptotic Fermat theorem, asymptotic Catalan conjecture and demonstrate the existence of infinitely many Wieferich primes. The main topic of the thesis is the radical of a perfect number. In the last chapter we derive some results, dealing with the distance between perfect numbers, incurred due to the abc conjecture.
Secondary keywords: arithmetic functions;prime numbers;perfect numbers;Mersenne primes;the abc conjecture;the radical;
URN: URN:SI:UM:
Type (COBISS): Undergraduate thesis
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: 47 f.
Keywords (UDC): mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;number theory;teorija števil;aritmetika;elementarna teorija števil;
ID: 8762256