Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

On a problem of Hajdu and Tengely

Title data

Siksek, Samir ; Stoll, Michael:
On a problem of Hajdu and Tengely.
In: Hanrot, Guillaume ; Morain, Francois ; Thomé, Emmanuel (Hrsg.): Algorithmic Number Theory : 9th international symposium, ANTS-IX, Nancy, France, July 19-23, 2010, proceedings. - Heidelberg : Springer , 2010 . - pp. 316-330 . - (Lecture Notes in Computer Science ; 6197 )
ISBN 978-3-642-14517-9
DOI: https://doi.org/10.1007/978-3-642-14518-6_25

Abstract in another language

We prove a result that finishes the study of primitive arithmetic progressions consisting of squares and fifth powers that was carried out by Hajdu and Tengely in a recent paper: The only arithmetic progression in coprime integers of the form (a², b², c², d⁵) is (1, 1, 1, 1). For the proof, we first reduce the problem to that of determining the sets of rational points on three specific hyperelliptic curves of genus 4. A 2-cover descent computation shows that there are no rational points on two of these curves. We find generators for a subgroup of finite index of the Mordell-Weil group of the last curve. Applying Chabauty’s method, we prove that the only rational points on this curve are the obvious ones.

Further data

Item Type: Article in a book
Refereed: Yes
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 01 Dec 2014 11:13
Last Modified: 01 Dec 2014 11:13
URI: https://eref.uni-bayreuth.de/id/eprint/4465