Domneva abc

diplomsko delo

Nataša Pavlič (Author), Daniel Eremita (Mentor)

Abstract

V diplomskem delu so uvodoma predstavljene osnove teorije števil ter osnove teorije grup in kolobarjev. V petem poglavju je izpeljan Masonov izrek, ki je polinomski analog domneve abc. Z uporabo Masonovega izreka je dokazan Fermatov veliki izrek za polinome. Osrednji del je namenjen obravnavi domneve abc. Ob predpostavki, da je domneva abc resnična izpeljemo asimptotično Catalanovo domnevo, asimptotični Fermatov veliki izrek in dokažemo obstoj neskončno mnogo Wieferichovih praštevil. Zadnje poglavje je namenjeno obravnavi kongruenčne domneve abc.

Keywords

matematika;domneve;kongruenca;praštevila;cela števila;polinomi;diofantske enačbe;diofantska analiza;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2011
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[N. Pavlič]
UDC:	51(043.2)
COBISS:	18386184
Views:	1818
Downloads:	139
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	THE ABC CONJECTURE
Secondary abstract:	At the beginning of the graduation thesis we present some basic notions and result of elementary number theory, group theory and ring theory. In the fifth chapter Mason's theorem is derived, which is a polynomial analogue of the abc conjecture. Using Mason's theorem we prove Fermat's last theorem for polynomials. The main part of the graduation thesis is devoted to the abc conjecture. We shall see that abc conjecture implies asimptotic Catalan conjecture, Fermat's last theorem and exsistance of infinitly many Wieferichh prime. In the last chapter we consider congruence abc conjecture.
Secondary keywords:	Mason's Theorem;The abc Conjecture;Fermat last theorem;Catalan conjecture;The Congruence abc Conjecture;Wieferich prime;Integer;polynomial;diophantine equation;diophantine analysis.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	58 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19280