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Title: DOMNEVA ABC Pavlič, Nataša (Author)Eremita, Daniel (Mentor) More about this mentor... UNI_Pavlic_Natasa_2011.pdf (443,85 KB)MD5: 078CAC3774BE356459E1F8A0B4C44439 Slovenian Undergraduate thesis (m5) FNM - Faculty of Natural Sciences and Mathematics 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. Masonov izrek, Domneva abc, Fermatov veliki izrek, Catalanova domneva, Wieferichovo praštevilo, Kongurenčna domneva abc, celo število, polinom, diofantska enačba, diofantska analiza. 2011 [N. Pavlič] Maribor 51(043.2) 18386184 URN:SI:UM:DK:O6NPD6EL 1724 135 FNM

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## Secondary language

Language: English THE ABC CONJECTURE 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. Mason's Theorem, The abc Conjecture, Fermat last theorem, Catalan conjecture, The Congruence abc Conjecture, Wieferich prime, Integer, polynomial, diophantine equation, diophantine analysis.