diplomsko delo
Marina Golob (Author), Daniel Eremita (Mentor)

Abstract

V diplomskem delu so obravnavane povezave med Catalanovimi števili, praštevili in praštevilskimi dvojčki. Prvo poglavje je namenjeno vpeljavi osnovnih pojmov in rezultatov, ki se uporabljajo v diplomskem delu. Predstavljeni so Wilsonov izrek, Eulerjev izrek ter mali Fermatov izrek. Glavna tema diplomskega dela je obravnavana v drugem poglavju. Prvi del tega poglavja je namenjen binomskim koeficientom in Catalanovim številom. Vpeljemo pojem Catalanovega psevdopraštevila, pojem Wieferichovega praštevila in predstavimo zvezo med tema pojmoma in pojmom psevdopraštevila. V drugem delu so obravnavani praštevilski dvojčki. Tretji del je namenjen povezavi med praštevili in različnimi kombinatoričnimi problemi, četrti del pa srednjemu binomskemu koeficientu v povezavi s Catalanovimi psevdopraštevili.

Keywords

Calatanova števila;kongruenca;praštevila;psevdopraštevila;praštevilski dvojček;binomski koeficient;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: [M. Golob]
UDC: 511(043.2)
COBISS: 19513352 Link will open in a new window
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Other data

Secondary language: English
Secondary title: CATALAN NUMBERS, PRIMES, AND TWIN PRIMES
Secondary abstract: The thesis considers connection between Catalan numbers, primes and twin primes. The first chapter introduces basic terms and results, which are used in the thesis. Wilson's theorem, Euler's theorem and Fermat's little theorem are presented. The main topic of the thesis is considered in the second chapter. Its first part is devoted to binomial coefficients and Catalan numbers. We introduce the concept of Catalan pseudoprime, the concept of Wieferich prime and present connection between these two concepts and the concept of pseudoprime. In the second part twin primes are considered. In its third part we focus on the connections between primes and various combinatorial problems, and in fourth part we observe the connections between the middle binomial coefficient and Catalan pseudoprimes.
Secondary keywords: Catalan number;congruence;prime;Wieferich prime;pseudoprime;Catalan pseudoprime;twin primes;the binomial coefficient.;
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: 999697