On a problem of Pethő. (November 2018)

• Record Type: Journal Article
• Authors: Tengely, Sz.; Ulas, M.
• Is Part Of: Journal of symbolic computation. Volume 89(2018)
• Page Start: 216
• Page End: 226
• Publication Date: 2018-11
• Subjects: primary 11D61 -- secondary 11Y50; Diophantine equations; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2017.11.013
• Languages: English
• ISSNs: 0747-7171

Abstract

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.