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On a problem of Hajdu and Tengely
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Siksek, Samir and Stoll, M. (Michael) (2010) On a problem of Hajdu and Tengely. In: 9th International Symposium on Algorithmic Number Theory, Inst Natl Rech Informat Automat, Nancy, France, 19-23 Jul 2010. Published in: Lecture Notes in Computer Science, Volume 6197 pp. 316-330. doi:10.1007/978-3-642-14518-6_25 ISSN 0302-9743.
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Abstract
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 (a(2),b(2),c(2),d(5)) 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.
Item Type: | Conference Item (Paper) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Series, Arithmetic, Numbers, Natural | ||||
Journal or Publication Title: | Lecture Notes in Computer Science | ||||
Publisher: | Springer | ||||
ISSN: | 0302-9743 | ||||
Official Date: | 2010 | ||||
Dates: |
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Volume: | Volume 6197 | ||||
Page Range: | pp. 316-330 | ||||
DOI: | 10.1007/978-3-642-14518-6_25 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Conference Paper Type: | Paper | ||||
Title of Event: | 9th International Symposium on Algorithmic Number Theory | ||||
Type of Event: | Other | ||||
Location of Event: | Inst Natl Rech Informat Automat, Nancy, France | ||||
Date(s) of Event: | 19-23 Jul 2010 |
Data sourced from Thomson Reuters' Web of Knowledge
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