Skip to Main content Skip to Navigation
Theses

Etudes sur les équations de Ramanujan-Nagell et de Nagell-Ljunggren ou semblables

Abstract : In this thesis, we study two types of diophantine equations. A first part of our study is about the resolution of the Ramanujan-Nagell equations $Cx^2+b^{2m}D=y^n$. A second part of our study is about the Nagell-Ljungren equations $\frac{x^p+y^p}{x+y}=p^ez^q$ including the diagonal case $p=q$. Our new results will be applied to the diophantine equations of the form $x^p+y^p=Bz^q$. The Fermat-Catalan equation (case $B=1$) will be the subject of a special study.
Document type :
Theses
Complete list of metadatas

Cited literature [75 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00429631
Contributor : Benjamin Dupuy <>
Submitted on : Tuesday, November 3, 2009 - 4:56:32 PM
Last modification on : Thursday, January 11, 2018 - 6:12:20 AM
Long-term archiving on: : Thursday, June 17, 2010 - 7:14:58 PM

Identifiers

  • HAL Id : tel-00429631, version 1

Collections

CNRS | IMB | INSMI

Citation

Benjamin Dupuy. Etudes sur les équations de Ramanujan-Nagell et de Nagell-Ljunggren ou semblables. Mathématiques [math]. Université Sciences et Technologies - Bordeaux I, 2009. Français. ⟨tel-00429631⟩

Share

Metrics

Record views

405

Files downloads

693