The Support Problem and Its Elliptic Analogue
| dc.contributor.author | Corrales Rodrigáñez, Carmen | |
| dc.contributor.author | Schoof, René | |
| dc.date.accessioned | 2023-06-20T18:41:42Z | |
| dc.date.available | 2023-06-20T18:41:42Z | |
| dc.date.issued | 1997 | |
| dc.description.abstract | Let F be a number field, Suppose x, y Є F* have the property that for all n Є Z and almost all prime ideals p of the ring of integers of F* one has that yn =1 (mod p) whenever xn=1 (mod p). We show that then y is a power of x. This answers a question of Erdos. We also prove an elliptic analogue of this result. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20271 | |
| dc.identifier.doi | 10.1006/jnth.1997.2114 | |
| dc.identifier.issn | 1096-1658 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0022314X97921144 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58330 | |
| dc.issue.number | 2 | |
| dc.journal.title | Journal of number theory | |
| dc.language.iso | eng | |
| dc.page.final | 290 | |
| dc.page.initial | 276 | |
| dc.publisher | Academic Press | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 511 | |
| dc.subject.keyword | Algebraic number | |
| dc.subject.keyword | Congruence | |
| dc.subject.keyword | Support problem | |
| dc.subject.keyword | Elliptic curves | |
| dc.subject.ucm | Teoría de números | |
| dc.subject.unesco | 1205 Teoría de Números | |
| dc.title | The Support Problem and Its Elliptic Analogue | |
| dc.type | journal article | |
| dc.volume.number | 64 | |
| dcterms.references | J. W. S. Cassels and A. Frohlich, Eds., ``Algebraic Number Theory,'' Academic Press,London/New York, 1967. G. Janusz, ``Algebraic Number Theory,'' Academic Press, New York/London, 1973. J. Silverman, ``The Arithmetic of Elliptic Curves,''Graduate Texts in Mathematics,Vol. 106, Springer-Verlag, Heidelberg/New York, 1986. A. Schinzel, On exponential congruences, Mat. Zametki, to appear. J.-P. Serre, Proprietes galoisiennes des points d'ordre fini des courbes elliptiques, Invent.Math. 15 (1972),259-331. (1uvres, III, Springer-Verlag, Berlin/Heidelberg/New York/Tokyo, 1986, 1-73.) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 9a5ad1cc-287e-48b3-83f9-e3d1e36d5ff2 | |
| relation.isAuthorOfPublication.latestForDiscovery | 9a5ad1cc-287e-48b3-83f9-e3d1e36d5ff2 |
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