Deljivost Fermatovih števil

diplomsko delo

Tadeja Sraka (Author), Daniel Eremita (Mentor)

Abstract

V diplomskem delu so uvodoma predstavljene osnove elementarne teorije števil, ki jih potrebujemo v diplomskem delu. V nadaljevanju obravnavamo Fermatova števila in spoznamo nekatere njihove osnovne lastnosti. Ogledali si bomo Pepinov test za ugotavljanje, kdaj je Fermatovo število praštevilo. V nadaljevanju sledi obravnava o deljivosti Fermatovih števil. Dokazali bomo Eulerjev in Lucasov izrek za deljivost Fermatovih števil. Ogledali si bomo povezavo med Fermatovimi števili in Wieferichovimi praštevili. Na koncu bomo predstavili, katera so zaenkrat edina sestavljena Fermatova števila, ki jih znamo popolnoma faktorizirati.

Keywords

matematika;Fermatovo število;praštevila;primitivni koreni;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2012
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[T. Sraka]
UDC:	511(043.2)
COBISS:	19849992
Views:	1662
Downloads:	190
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	DIVISIBILITY OF FERMAT NUMBERS
Secondary abstract:	In the introduction this thesis presents the fundamentals of elementary number theory which are applied troughout the thesis. Next, we consider Fermat numbers by presenting some of their basic properties. Pepin's test to determine the primality of a Fermat number is presented. It is followed by a discussion on divisibility of Fermat numbers. The proof of Euler's and Lucas's theorem on divisibility of Fermat numbers is examined. It introduces the connection between Fermat numbers and Wieferich prime numbers. At the end we present a list of composite Fermat numbers for which the complete factorization is known.
Secondary keywords:	Prime;congruence;Fermat’s little theorem;ord number;primitive root;kth power residue;Fermat number;Wieferich prime .;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	50 f.
ID:	8723117