International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 6, Pages 349-353
doi:10.1155/S0161171202007561
On the roots of the substitution Dickson polynomials
Department of Mathematics, The Pennsylvania State University, New Kensington Campus, New Kensington 15068, PA, USA
Received 10 April 2001
Copyright © 2002 Javier Gomez-Calderon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We show that under the composition of multivalued functions, the
set of the y-radical roots of the Dickson substitution
polynomial gd(x,a)−gd(y,a) is generated by one of the roots. Hence, we show an expected generalization of the fact that, under the composition of the functions, the y-radical
roots of xd−yd are generated by ζdy.