Revisiting the Fermat-type equation $x^{13} + y^{13} = 3z^7$
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915556176691200 |
|---|---|
| author | Billerey, Nicolas Chen, Imin Dembélé, Lassina Dieulefait, Luis Freitas, Nuno |
| author_facet | Billerey, Nicolas Chen, Imin Dembélé, Lassina Dieulefait, Luis Freitas, Nuno |
| contents | We solve the Fermat-type equation \[ x^{13} + y^{13} = 3 z^7, \qquad \gcd(x,y,z) = 1 \] combining a unit sieve, the multi-Frey modular method, level raising, computations of systems of eigenvalues modulo 7 over a totally real field, and results for reducibility of certain Galois representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13773 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting the Fermat-type equation $x^{13} + y^{13} = 3z^7$ Billerey, Nicolas Chen, Imin Dembélé, Lassina Dieulefait, Luis Freitas, Nuno Number Theory Primary 14D1, Secondary 11F80 We solve the Fermat-type equation \[ x^{13} + y^{13} = 3 z^7, \qquad \gcd(x,y,z) = 1 \] combining a unit sieve, the multi-Frey modular method, level raising, computations of systems of eigenvalues modulo 7 over a totally real field, and results for reducibility of certain Galois representations. |
| title | Revisiting the Fermat-type equation $x^{13} + y^{13} = 3z^7$ |
| topic | Number Theory Primary 14D1, Secondary 11F80 |
| url | https://arxiv.org/abs/2510.13773 |