Glasnik Matematicki, Vol. 44, No.2 (2009), 309-321.

SOLUTIONS OF A CLASS OF QUARTIC THUE INEQUALITIES

Bo He, Borka Jadrijević and Alain Togbé

Department of Mathematics, ABa Teacher's College, Wenchuan, Sichuan, 623000, P. R. China
e-mail: bhe@live.cn

Faculty of Science, Department of Mathematics, University of Split, Teslina 12, 21000 Split, Croatia
e-mail: borka@pmfst.hr

Mathematics Department, Purdue University North Central, 1401 S, U.S. 421, Westville IN 46391, USA
e-mail: atogbe@pnc.edu

Abstract.   Let c be a positive integer. In this paper, we use the method of Tzanakis to transform the quartic Thue inequality

|x4 - 4x3y - (2c-2)x2y2 + (4c+4)xy3 - (2c-1)y4| ≤ max{c/4, 4}

into systems of Pellian equations. Then we find all primitive solutions of this inequality using continued fractions.

2000 Mathematics Subject Classification.   11D59, 11D09, 11D75, 11A55.

Key words and phrases.   Thue inequalities, method of Tzanakis, continued fractions.

Full text (PDF) (free access)

DOI: 10.3336/gm.44.2.04

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