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Cyclotomic Norm Diophantine Equations

dc.contributor.advisorMihailescu, Preda Prof. Dr.
dc.contributor.authorChen, Han
dc.date.accessioned2023-10-25T12:22:22Z
dc.date.available2023-11-01T00:50:09Z
dc.date.issued2023-10-25
dc.identifier.urihttp://resolver.sub.uni-goettingen.de/purl?ediss-11858/14935
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-10158
dc.format.extent63de
dc.language.isoengde
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subject.ddc510de
dc.titleCyclotomic Norm Diophantine Equationsde
dc.typedoctoralThesisde
dc.contributor.refereeMihailescu, Preda Prof. Dr.
dc.date.examination2023-09-28de
dc.description.abstractengIn this thesis, I consider two Diophantine norm equations. For the equation of the Nagell-Ljunggren equation $\frac{x^p-1}{x-1} = p^e y^q$ with distinct odd prime exponents $p, q$, I show that, for $p > 3$, it has no solutions under the condition that $q$ does not divide $h_p^-$, the minus part of the class number of the $p$-th cyclotomic field. For the equation of the generalized Ramanujan-Nagell equation $x^2+C=y^p$ with positive integer $C$ and odd prime exponent $p$, I use the theory of Primitive Divisor Theorem for Lucas sequences to find all the positve integer solutions under some congruence conditions.de
dc.contributor.coRefereeBrüdern, Jörg Prof. Dr.
dc.subject.engNagell-Ljunggren equationde
dc.subject.engThe generalized Ramanujan-Nagell equationde
dc.subject.engClass field theoryde
dc.identifier.urnurn:nbn:de:gbv:7-ediss-14935-5
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de
dc.description.embargoed2023-11-01de
dc.identifier.ppn187049699X
dc.notes.confirmationsentConfirmation sent 2023-10-25T12:45:01de


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