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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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WRAP-Fermat’s-equation-quadratic-imaginary-number-fields-Turcas-2018.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (603Kb) | Preview |
Official URL: http://dx.doi.org/10.1007/s40993-018-0117-y
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 | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||||||
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| 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: |
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