20.500.12556/DKUM-18121 DOMNEVA ABC THE ABC CONJECTURE V diplomskem delu uvodoma so predstavljene osnove teorije števil ter osnove teorije grup in kolobarjev. V petem poglavju je izpeljan Masonov izrek, ki je polinomski analog domneve abc.Z uporabo Masonovega izreka je dokazan Fermatov veliki izrek za polinome. Osrednji del je namenjen obravnavi domneve abc. Ob predpostavki, da je domneva abc resnična izpeljemo asimptotično Catalanovo domnevo, asimptotični Fermatov veliki izrek in dokažemo obstoj neskončno mnogo Wieferichovih praštevil. Zadnje poglavje je namenjeno obravnavi kongruenčne domneve abc. At the beginning of the graduation thesis we present some basic notions and result of elementary number theory, group theory and ring theory. In the fifth chapter Mason's theorem is derived, which is a polynomial analogue of the abc conjecture. Using Mason's theorem we prove Fermat's last theorem for polynomials. The main part of the graduation thesis is devoted to the abc conjecture. We shall see that abc conjecture implies asimptotic Catalan conjecture, Fermat's last theorem and exsistance of infinitly many Wieferichh prime. In the last chapter we consider congruence abc conjecture. Masonov izrek Domneva abc Fermatov veliki izrek Catalanova domneva Wieferichovo praštevilo Kongurenčna domneva abc celo število polinom diofantska enačba diofantska analiza. Mason's Theorem The abc Conjecture Fermat last theorem Catalan conjecture The Congruence abc Conjecture Wieferich prime Integer polynomial diophantine equation diophantine analysis. true true false [N. Pavlič] Slovenski jezik Angleški jezik Diplomsko delo 2011-04-18 00:29:17 2011-05-23 14:33:23 2022-04-13 10:27:03 2023-12-23 03:22:50 2011 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 18386184 URN:SI:UM:DK:O6NPD6EL UNI_Pavlic_Natasa_2011.pdf UNI_Pavlic_Natasa_2011.pdf 1 078CAC3774BE356459E1F8A0B4C44439 df66bd83a7c8c734ab23440a0d629119ef8157771ce0088bea7923c1a1bff870 0d8a9858-7c05-11eb-bb7a-00155d0001ca 20.500.12556/dkum/bb05a970-863a-4c79-a811-c216ddb02223 https://dk.um.si/Dokument.php?lang=slv&id=21535 Fakulteta za naravoslovje in matematiko 0 0 0