✦ LIBER ✦
Undecidable and decidable restrictions of Hilbert's Tenth Problem: images of polynomials vs. images of exponential functions
✍ Scribed by Mihai Prunescu
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 112 KB
- Volume
- 52
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
Dedicated to Professor Günter Asser on the occasion of his eightieth birthday
Classical results of additive number theory lead to the undecidability of the existence of solutions for diophantine equations in given special sets of integers. Those sets which are images of polynomials are covered by a more general result in the second section. In contrast, restricting diophantine equations to images of exponential functions with natural bases leads to decidable problems, as proved in the third section.