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AuthorHeinlein, Matthiasdc.contributor.author
Date of accession2016-03-15T09:04:19Zdc.date.accessioned
Available in OPARU since2016-03-15T09:04:19Zdc.date.available
Year of creation2013dc.date.created
AbstractWe define the set P_a as the divisors of a^n+1 where a is a fixed natural number and n is any natural number. One is interested in criteria to find out if a certain number d is in the set P_a or not. This question is very related to the term of the multiplicative order in Z/dZ. The author shows that it is only necessary to know about the primes in P_a and then one can easily check if any number d is in P_a or not. The main idea of the work is to look at certain similarities between the set P_a and the set of prime numbers. One can formulate statement for P_a-numbers which is very similar to the Goldbach´s conjecture and twin prime conjecture for prime numbers. The last part of this thesis deals with the set Q_d which contains all bases a with a^n+1 is divisible by d for a certain n. Looking for sets Q_d with "a maximum amount of elements" leads to the unsolved problem of Fermat prime numbers 2^(2^n)+1.dc.description.abstract
Languagededc.language.iso
PublisherUniversität Ulmdc.publisher
LicenseStandarddc.rights
Link to license texthttps://oparu.uni-ulm.de/xmlui/license_v3dc.rights.uri
KeywordElegant numbersdc.subject
KeywordGood numbersdc.subject
KeywordP_a numbersdc.subject
Dewey Decimal GroupDDC 510 / Mathematicsdc.subject.ddc
LCSHNumber theorydc.subject.lcsh
LCSHOrderdc.subject.lcsh
TitleErgebnisse über die Teiler der Folgen (a^n+1)dc.title
Resource typeAbschlussarbeit (Bachelor)dc.type
DOIhttp://dx.doi.org/10.18725/OPARU-2560dc.identifier.doi
PPN823310760dc.identifier.ppn
URNhttp://nbn-resolving.de/urn:nbn:de:bsz:289-vts-87965dc.identifier.urn
GNDZahlentheoriedc.subject.gnd
FacultyFakultät für Mathematik und Wirtschaftswissenschaftenuulm.affiliationGeneral
Date of activation2015-04-20T08:26:34Zuulm.freischaltungVTS
Peer reviewneinuulm.peerReview
DCMI TypeTextuulm.typeDCMI
VTS ID8796uulm.vtsID
CategoryPublikationenuulm.category
Bibliographyuulmuulm.bibliographie


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