Salah Eddine Rihane, Mohand Ouamar Hernane and Alain Togbé

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 4, Pages 1–14

DOI: 10.7546/nntdm.2021.27.4.1-14

**Full paper (PDF, 249 Kb)**

## Details

### Authors and affiliations

Salah Eddine Rihane

*Department of Mathematics and Computer Science
Abdelhafid Boussouf University
Mila 43000, Algeria*

Mohand Ouamar Hernane

*Université des Sciences et de la Technologie Houari-Boumedièene (USTHB),
Faculté de Mathématiques, Laboratoire d’Algèbre et Théorie des Nombres
BP 32, 16111 Bab-Ezzouar, Alger, Algerie
*

Alain Togbé

*Department of Mathematics, Statistics
Purdue University Northwest
1401 S, U.S. 421, Westville IN 46391, United States
*

### Abstract

Let be an integer. In this paper, we use the method of Tzanakis to transform the quartic Thue equation into systems of Pell equations. Then, we determine all primitive solutions with .

### Keywords

- Parametric Thue equations
- Method of Tzanakis
- Continued fraction
- Linear form in logarithms

### 2020 Mathematics Subject Classification

- 11D59
- 11D09

- 11D75
- 11D25
- 11A55
- 11J86

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## Cite this paper

Rihane, S. E., Hernane, M. O., & Togbé, A. (2021). A parametric family of quartic Thue inequalities. *Notes on Number Theory and Discrete Mathematics*, 27(4), 1-14, DOI: 10.7546/nntdm.2021.27.4.1-14.