## Title data

Freitas, Nuno ; Siksek, Samir:

**Fermat’s last theorem over some small real quadratic fields.**

*In:* Algebra & Number Theory.
Vol. 9
(2015)
Issue 4
.
- pp. 875-895.

ISSN 1937-0652

DOI: https://doi.org/10.2140/ant.2015.9.875

## Project information

Project title: |
Project's official title Project's id Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory SPP 1489 |
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Project financing: |
Deutsche Forschungsgemeinschaft |

## Abstract in another language

Using modularity, level lowering, and explicit computations with Hilbert modular forms, Galois representations, and ray class groups, we show that for 3 ≤ d ≤ 23, where d ≠ 5, 17 and is squarefree, the Fermat equation x^n + y^n = z^n has no nontrivial solutions over the quadratic field ℚ(d) for n ≥ 4. Furthermore, we show that for d = 17, the same holds for prime exponents n ≡ 3,5 (mod 8).

## Further data

Item Type: | Article in a journal |
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Refereed: | Yes |

Keywords: | Fermat; modularity; Galois representation; level lowering |

Subject classification: | Mathematical Subject Classification 2010: 11D41 (11F80, 11F03) |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 12 Apr 2016 07:37 |

Last Modified: | 12 Apr 2016 07:37 |

URI: | https://eref.uni-bayreuth.de/id/eprint/32159 |