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master's thesis
Balansirajući brojevi
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:509781
Plantak, Lucija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Plantak, L. (2020). Balansirajući brojevi (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:509781

Plantak, Lucija. "Balansirajući brojevi." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:509781

Plantak, Lucija. "Balansirajući brojevi." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:509781

Plantak, L. (2020). 'Balansirajući brojevi', Master's thesis, University of Zagreb, Faculty of Science, accessed 06 October 2024, https://urn.nsk.hr/urn:nbn:hr:217:509781

Plantak L. Balansirajući brojevi [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 October 06] Available at: https://urn.nsk.hr/urn:nbn:hr:217:509781

L. Plantak, "Balansirajući brojevi", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:509781

Metadata
TitleBalansirajući brojevi
Title (english)Balancing numbers
AuthorLucija Plantak
MentorZrinka Franušić (mentor)
Committee memberZrinka Franušić (predsjednik povjerenstva)
Committee memberFilip Najman (član povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
Committee memberTomislav Pejković (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-09-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu definiramo balansirajući broj \( n \in \mathbb{N}\) kao rješenje diofantske jednadžbe 1 + 2 + ... + (n + 1) = (n + 1) + (n + 2) + ... + (n + r); gdje je \( r \in \mathbb{N}_0\) balanser pridružen broju \( n \). Na primjer, 1; 6; 35 i 204 su balansirajući brojevi s balanserima 0; 2; 14 and 84, redom. Zanimljivo je da balansirajući brojevi zadovoljavaju linearnu rekurzivnu relaciju \(B_{n+1} = 6B_{n} - B_{n-1} , n \in \mathbb{N}\). Pokazat ćemo neka svojstva balansirajućih brojeva i ustanoviti povezanost s nekim klasičnim diofanstskim jednadžbama. Također, definirat ćemo kobalansirajuće brojeve malo modificirajući jednadžbu za balansirajuće brojeve i promatrat ćemo njihova svojstva.
Abstract (english)
In this thesis we define balancing numbers\( n \in \mathbb{N}\) as a solution of the Diophantine equation 1 + 2 + ... + (n + 1) = (n + 1) + (n + 2) + ... + (n + r); calling \( r \in \mathbb{N}_0\) the balancer corresponding to \( n \). For example, 1; 6; 35 and 204 are balancing numbers with balancers 0; 2; 14 and 84, respectively. It is interesting that the balancing numbers satisfy linear recurrence relation \(B_{n+1} = 6B_{n}-B_{n-1} , n \in \mathbb{N}\). We show properties of balancing numbers and establish relation to some classic Diophantine equation. Also, we define the cobalancing numbers by slightly modifying equation for balancing numbers and observe their properties.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:509781
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-03-11 11:58:49