The Diophantine equation $aX^{4} - bY^{2} = 1$
| dc.creator | Akhtari, Shabnam | |
| dc.date | 2009-03-10 | |
| dc.date.accessioned | 2026-07-07T12:50:53Z | |
| dc.date.available | 2026-07-07T12:50:53Z | |
| dc.description | As an application of the method of Thue-Siegel, we will resolve a conjecture of Walsh to the effect that the Diophantine equation $aX^{4} - bY^2=1$, for fixed positive integers $a$ and $b$, possesses at most two solutions in positive integers $X$ and $Y$. Since there are infinitely many pairs $(a,b)$ for which two such solutions exist, this result is sharp. | |
| dc.description | 20 pages, To appear in Journal fur die Reine und Angewandte Mathematik (Crelle's Journal) | |
| dc.identifier | https://arxiv.org/abs/0903.1742 | |
| dc.identifier | http://arxiv.org/abs/0903.1742 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222819 | |
| dc.subject | Number Theory | |
| dc.subject | 11D25, 11D41, 11B39, 11J25 | |
| dc.title | The Diophantine equation $aX^{4} - bY^{2} = 1$ | |
| dc.type | text |