Alspachova neenakost

diplomsko delo

Sandra Čepe (Author), Daniel Eremita (Mentor)

Abstract

Osrednja tema diplomskega dela je dokaz Alspachove neenakosti in iskanje zgornjih mej vsote glavnih deliteljev. Dokazano je, da je vsako liho naravno število n > 15, ki ni potenca praštevila, večje od dvakratnika vsote glavnih deliteljev števila n. V diplomskem delu so v uvodnih treh poglavjih predstavljeni osnovni pojmi elementarne teorije števil, aritmetične funkcije, popolna števila in Mersennova praštevila. V četrtem poglavju so obravnavani Alspachova neenakost, Bernoulli-Weierstrassova neenakost, aritmetična in geometrijska sredina. Izpeljane so tudi nekatere bolj natančne zgornje meje vsote glavnih deliteljev.

Keywords

matematika;praštevila;aritmetika;funkcije;popolna števila;Alspachova neenakost;aritmetična sredina;geometrijska sredina;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2013
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[S. Čepe]
UDC:	51(043.2)
COBISS:	19747080
Views:	1290
Downloads:	123
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Alspach's inequality
Secondary abstract:	Main topic of the graduation thesis is to present a proof of Alspach's inequality and to obtain some further upper bounds on the sum of principal divisors of an integer. We prove, that any odd integer n > 15 that is not a prime-power is greater than twice the sum of its principal divisors. In the first three chapters of the thesis we present basic notions and results of elementary number theory, arithemtic functions, perfect numbers and Mersenne primes numbers. In the fourth chapter we consider Alspach's inequality, Bernoulli- Weierstarss inequality, arithmetic and geometric mean. Some stronger upper bounds on sums of principal divisors are also obtained.
Secondary keywords:	primes;arithmetic functions;perfect numbers;Mersenne primes;Alspach's inequality;arithmetic and geometric mean.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	39 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	1027264