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Title:NERAZCEPNI BIKVADRATNI POLINOMI, KI SO RAZCEPNI PO POLJUBNEM MODULU p
Authors:Kline, Jasmina (Author)
Eremita, Daniel (Mentor) More about this mentor... New window
Files:.pdf UNI_Kline_Jasmina_2010.pdf (880,27 KB)
 
Language:Slovenian
Work type:Undergraduate thesis (m5)
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:V diplomskem delu je obravnavan problem razcepnosti bikvadratnih polinomov s celoštevilskimi koeficienti. V prvem poglavju so predstavljeni pojmi in rezultati s področja teorije kongruenc, ki so potrebni za nadaljnjo obravnavo. V drugem poglavju so vpeljani pojmi in rezultati s področja polinomov z racionalnimi koeficienti, v tretjem poglavju pa polinomske kongruence na množici vseh polinomov s celoštevilskimi koeficienti. Osrednji del diplomskega dela je namenjen obravnavi bikvadratnih polinomov, ki so nerazcepni v Z[x], vendar so razcepni po modulu p za vsako praštevilo p. V zadnjem poglavju so obravnavani taki nerazcepni bikvadratni polinomi, ki so razcepni po modulu n za vsako naravno število n>1.
Keywords:bikvadratni polinom, kongruenca, polinom, kvadratni ostanek, Legendrov simbol
Year of publishing:2010
Publisher:[J. Kline]
Source:Maribor
UDC:51(043.2)
COBISS_ID:17982984 Link is opened in a new window
NUK URN:URN:SI:UM:DK:ETQSAT2J
Views:1555
Downloads:154
Metadata:XML RDF-CHPDL DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:IRREDUCIBLE BIQUADRATIC POLYNOMALS WITH FACTORIZATIONS MODULO p
Abstract:The graduation thesis discusses a problem of irreducible biquadratic polynomials with integer coefficients. In the first chapter the theory of congruences is introduced. The second chapter is devoted to the theory of polynomials with rational coefficients. Next, we consider polynomial congruences on the set of all polynomials with integer coefficients. The main part of the thesis deals with biquadratic polynomials which are irreducible in Z[x], but reducible modulo p for every prime number p. In the last chapter we consider irreducible biquadratic polynomials that are reducible modulo n for every integer n>1.
Keywords:biquadratic polynomial, congruence, polynomial, quadratic residue, Legendre symbol


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