International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 6, Pages 349-353

On the roots of the substitution Dickson polynomials

Javier Gomez-Calderon

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.


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 xdyd are generated by ζdy.