A parametric family of quintic Thue equations

Authors:
István Gaál and Günter Lettl

Journal:
Math. Comp. **69** (2000), 851-859

MSC (1991):
Primary 11D57; Secondary 11Y50

DOI:
https://doi.org/10.1090/S0025-5718-99-01155-2

Published electronically:
May 24, 1999

MathSciNet review:
1659855

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Abstract | References | Similar Articles | Additional Information

Abstract: For an integral parameter we investigate the family of Thue equations

originating from Emma Lehmer's family of quintic fields, and show that for the only solutions are the trivial ones with or . Our arguments contain some new ideas in comparison with the standard methods for Thue families, which gives this family a special interest.

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Additional Information

**István Gaál**

Affiliation:
Kossuth Lajos University, Mathematical Institute, H–4010 Debrecen Pf.12., Hungary

Email:
igaal@math.klte.hu

**Günter Lettl**

Affiliation:
Karl-Franzens-Universität Graz, Institut für Mathematik, A–8010 Graz, Heinrichstraße 36, Austria

Email:
guenter.lettl@kfunigraz.ac.at

DOI:
https://doi.org/10.1090/S0025-5718-99-01155-2

Keywords:
Parametric Thue equation,
Baker's method

Received by editor(s):
December 12, 1997

Received by editor(s) in revised form:
July 14, 1998

Published electronically:
May 24, 1999

Additional Notes:
The first author’s research was supported in part by Grants 16791 and 16975 from the Hungarian National Foundation for Scientific Research

Article copyright:
© Copyright 2000
American Mathematical Society