Original scientific paper

https://doi.org/10.3336/gm.44.2.04

Solutions of a class of quartic Thue inequalities

Bo He ; Department of Mathematics, ABa Teacher's College, Wenchuan, Sichuan, 623000, P. R. China
Borka Jadrijević orcid.org/0000-0002-5913-3719 ; Faculty of Science, Department of Mathematics, University of Split, Teslina 12, 21000 Split, Croatia
Alain Togbe orcid.org/0000-0002-5882-936X ; Mathematics Department, Purdue University North Central, 1401 S, U.S. 421, Westville IN 46391, USA

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.

Keywords

Thue inequalities; method of Tzanakis; continued fractions

Hrčak ID:

44048

URI

https://hrcak.srce.hr/44048

Publication date:

9.12.2009.

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