✦ LIBER ✦
Solving Genus Zero Diophantine Equations with at Most Two Infinite Valuations
✍ Scribed by Dimitrios Poulakis; Evaggelos Voskos
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 249 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0747-7171
No coin nor oath required. For personal study only.
✦ Synopsis
Let f (X, Y ) be an absolutely irreducible polynomial with integer coefficients such that the curve defined by the equation f (X, Y ) = 0 is of genus 0 having at most two infinite valuations. This paper describes a practical general method for the explicit determination of all integer solutions of the diophantine equation f (X, Y ) = 0. Several elaborated examples are given. Furthermore, a necessary and sufficient condition for a curve of genus 0 to have infinitely many integer points is obtained.