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Faktorizacija naravnih števil z binarnimi kvadratnimi formami : magistrsko delo : na študijskem programu 2. stopnje MatematikaKušek, AlenV magistrskem delu obravnavmo faktorizacijo naravnih števil oblike ▫$mx^2 + ny^2$▫. Delo je razdeljeno na štiri poglavja. V prvem poglavju spoznamo Fermatovo faktorizacijsko metodo in Gaussova cela ... števila. V drugem poglavju se ukvarjamo s faktorizacijo števil oblike ▫$mx^2 + ny^2$▫. Predstavljena je Eulerjeva formula, s katero je mogoče faktorizirati števila oblike ▫$mx^2 + ny^2$▫. Prav tako obravnavamo sodobnejšo metodo faktorizacije, ki sta jo razvila Lucas in Mathews. Pred-stavljen je enostaven dokaz njunega izreka, ki ga je podal Brillhart. V tretjem poglavju raziskujemo faktorizacijo lihega naravnega števila, ki ga lahko zapišemo s kvadratno formo ▫$mx^2 + ny^2$▫ na dva različna načina, kjer sta ▫$m$▫ in ▫$n$▫ naravni števili. Pri tem podamo eksplicitno formulo za faktorizacijo in pogoje za kvadratno formo, ki so potrebni za obstoj te formule. Pri tem bomo uporabljali rezultate prejšnjega poglavja. V zadnjem poglavju obravnavamo podoben problem kot v tretjem poglavju, le da tokrat predpostavimo, da je ▫$n$▫ negativno celo število.Type of material - master's thesis ; adult, seriousPublication and manufacture - Maribor : [A. Kušek], 2018Language - slovenianCOBISS.SI-ID - 24020232
Author
Kušek, Alen
Other authors
Eremita, Daniel
Topics
Univerzitetna in visokošolska dela |
magistrska dela |
elementarna teorija števil |
faktorizacija naravnih števil |
Eulerjeva formula |
kvadratna forma |
master theses |
elementary number theory |
factoring of integers |
Euler's formula |
quadratic formula
Library/institution |
City | Acronym | For loan | Other holdings |
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Miklošič Library FPNM, Maribor | Maribor | PEFMB |
reading room 1 cop.
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JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
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DRS, in which the journal is indexed
Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Kušek, Alen | |
Eremita, Daniel | 19550 |
Source: Personal bibliographies
and: SICRIS
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