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On Fermat’s equation over some quadratic imaginary number fields

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Ţurcaş, George C. (2018) On Fermat’s equation over some quadratic imaginary number fields. Research in Number Theory, 4 (2). 24. doi:10.1007/s40993-018-0117-y

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Official URL: http://dx.doi.org/10.1007/s40993-018-0117-y

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Abstract

Assuming a deep but standard conjecture in the Langlands programme, we prove Fermat’s Last Theorem over Q(i). Under the same assumption, we also prove that, for all prime exponents p ≥ 5, Fermat’s equation a^p+ b^p+ c^p = 0 does not have non-trivial solutions over Q(√(-2)) and Q(√(-7)).

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Fermat's last theorem, Galois modules (Algebra), Quadratic fields
Journal or Publication Title: Research in Number Theory
Publisher: SpringerOpen
ISSN: 2363-9555
Official Date: June 2018
Dates:
DateEvent
June 2018Published
4 May 2018Available
25 April 2018Accepted
Volume: 4
Number: 2
Article Number: 24
DOI: 10.1007/s40993-018-0117-y
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
PhD studentship[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266

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