## Experimental Mathematics

- Experiment. Math.
- Volume 15, Number 1 (2006), 1-6.

### Diophantine Equations over Global Functions Fields II: R-Integral Solutions of Thue Equations

#### Abstract

Let {\small $K$} be an algebraic function field over a finite field. Let {\small $L$} be an extension field of {\small $K$} of degree at least 3. Let {\small $R$} be a finite set of valuationsof {\small $K$} and denote by {\small $S$} the set of extensions of valuations of {\small $R$} to {\small $L$}. Denote by {\small $O_{K,R},O_{L,S}$} the ring of {\small $R$}-integers of {\small $K$} and {\small $S$}-integers of {\small $L$}, respectively. Assume that {\small $\alpha\in O_{L,S}$} with {\small $L=K(\alpha)$}, let {\small $0\neq \mu\in O_{K,R}$}, and consider the solutions {\small $(x,y)\in O_{K,R}$} of the Thue equation

{\small \[ N_{L/K}(x-\alpha y)=\mu.\]}

We give an efficient method for calculating the {\small $R$}-integral solutions of the above equation. The method is different from that in our previous paper and is much more efficient in many cases.

#### Article information

**Source**

Experiment. Math., Volume 15, Number 1 (2006), 1-6.

**Dates**

First available in Project Euclid: 16 June 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1150476898

**Mathematical Reviews number (MathSciNet)**

MR2229380

**Zentralblatt MATH identifier**

1142.11019

**Subjects**

Primary: 11D59: Thue-Mahler equations 11Y50: Computer solution of Diophantine equations 11R58: Arithmetic theory of algebraic function fields [See also 14-XX]

**Keywords**

Thue equations global function fields

#### Citation

GaÁl, IstvÁn; Pohst, Michael. Diophantine Equations over Global Functions Fields II: R-Integral Solutions of Thue Equations. Experiment. Math. 15 (2006), no. 1, 1--6. https://projecteuclid.org/euclid.em/1150476898