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On a problem of Pethő.
- Source :
-
Journal of Symbolic Computation . Nov2018, Vol. 89, p216-226. 11p. - Publication Year :
- 2018
-
Abstract
- In this paper we deal with a problem of Pethő related to existence of a quartic algebraic integer α for which β = 4 α 4 α 4 − 1 − α α − 1 is a quadratic algebraic number. By studying rational solutions of certain Diophantine system we prove that there are infinitely many α 's such that the corresponding β is quadratic. Moreover, we present a description of quartic numbers α such that the corresponding β is a quadratic real number. [ABSTRACT FROM AUTHOR]
- Subjects :
- *QUARTIC equations
*ALGEBRA
*DIOPHANTINE analysis
*MATHEMATICS
*INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 07477171
- Volume :
- 89
- Database :
- Academic Search Index
- Journal :
- Journal of Symbolic Computation
- Publication Type :
- Academic Journal
- Accession number :
- 129714439
- Full Text :
- https://doi.org/10.1016/j.jsc.2017.11.013