✦ LIBER ✦
When Newton met Diophantus: A Study of Rational-Derived Polynomials and Their Extension to Quadratic Fields
✍ Scribed by Ralph H Buchholz; James A MacDougall
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 311 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
We consider the problem of classifying all univariate polynomials, defined over a domain k, with the property that they and all their derivatives have all their roots in k. This leads to a number of interesting sub-problems such as finding k-rational points on a curve of genus 1 and rational points on a curve of genus 2. 2000