Quartic polynomials with a given discriminant
| dc.contributor.author | Klaška, Jiří | cs |
| dc.coverage.issue | 1 | cs |
| dc.coverage.volume | 72 | cs |
| dc.date.accessioned | 2022-03-14T11:53:31Z | |
| dc.date.available | 2022-03-14T11:53:31Z | |
| dc.date.issued | 2022-02-21 | cs |
| dc.description.abstract | Let $ 0\ne D \in \Bbb Z$ and let $Q_D$ be the set of all monic quartic polynomials $ x^4 +ax^3 +bx^2 + cx + d \in \Bbb Z[x]$ with the discriminant equal to $D$. In this paper we will devise a method for determining the set $Q_D$. Our method is strongly related to the theory of integral points on elliptic curves. The well-known Mordell's equation plays an important role as well in our considerations. Finally, some new conjectures will be included inspired by extensive calculation on a computer. | en |
| dc.format | text | cs |
| dc.format.extent | 35-50 | cs |
| dc.format.mimetype | application/pdf | cs |
| dc.identifier.citation | Mathematica Slovaca. 2022, vol. 72, issue 1, p. 35-50. | en |
| dc.identifier.doi | 10.1515/ms-2022-0003 | cs |
| dc.identifier.issn | 1337-2211 | cs |
| dc.identifier.other | 176796 | cs |
| dc.identifier.uri | http://hdl.handle.net/11012/203964 | |
| dc.language.iso | en | cs |
| dc.publisher | De Gruyter | cs |
| dc.relation.ispartof | Mathematica Slovaca | cs |
| dc.relation.uri | https://www.degruyter.com/document/doi/10.1515/ms-2022-0003/html | cs |
| dc.rights | Creative Commons Attribution 4.0 International | cs |
| dc.rights.access | openAccess | cs |
| dc.rights.sherpa | http://www.sherpa.ac.uk/romeo/issn/1337-2211/ | cs |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | cs |
| dc.subject | quartic polynomial | en |
| dc.subject | discriminant | en |
| dc.subject | Mordell's equation | en |
| dc.subject | elliptic curve | en |
| dc.title | Quartic polynomials with a given discriminant | en |
| dc.type.driver | article | en |
| dc.type.status | Peer-reviewed | en |
| dc.type.version | publishedVersion | en |
| sync.item.dbid | VAV-176796 | en |
| sync.item.dbtype | VAV | en |
| sync.item.insts | 2022.03.23 16:56:01 | en |
| sync.item.modts | 2022.03.23 16:15:05 | en |
| thesis.grantor | Vysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematiky | cs |
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