✦ LIBER ✦
Complete decomposition of Dickson-type polynomials and related Diophantine equations
✍ Scribed by Thomas Stoll
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 237 KB
- Volume
- 128
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
We characterize decomposition over C of polynomials f (a,B) n (x) defined by the generalized Dicksontype recursive relation (n 1)
where B, a ∈ Q or R. As a direct application of the uniform decomposition result, we fully settle the finiteness problem for the Diophantine equation
This extends and completes work of Dujella/Tichy and Dujella/Gusić concerning Dickson polynomials of the second kind. The method of the proof involves a new sufficient criterion for indecomposability of polynomials with fixed degree of the right component.