20.500.12556/DKUM-16472 NERAZCEPNI BIKVADRATNI POLINOMI, KI SO RAZCEPNI PO POLJUBNEM MODULU p IRREDUCIBLE BIQUADRATIC POLYNOMALS WITH FACTORIZATIONS MODULO p 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. 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. bikvadratni polinom kongruenca polinom kvadratni ostanek Legendrov simbol biquadratic polynomial congruence polynomial quadratic residue Legendre symbol true true false [J. Kline] Slovenski jezik Angleški jezik Diplomsko delo 2010-10-20 19:28:54 2010-11-18 15:44:04 2022-04-13 08:11:46 2023-12-20 03:35:16 2010 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 17982984 URN:SI:UM:DK:ETQSAT2J UNI_Kline_Jasmina_2010.pdf UNI_Kline_Jasmina_2010.pdf 1 6FC3B07A6B1962FF582951E982E71203 5597f2ab893736b9b1adb6603c876bde400fea11687980166bcf59730e798c23 a7e1c9e4-7c04-11eb-bb7a-00155d0001ca 20.500.12556/dkum/38774f18-770f-4828-8418-39cc48a53e1f https://dk.um.si/Dokument.php?lang=slv&id=18692 Fakulteta za naravoslovje in matematiko 0 0 0