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Journal of Applied Mathematics
Volume 2013, Article ID 472350, 7 pages
Research Article

Fixed Points of the Dickson Polynomials of the Second Kind

Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 17551, Al Ain, Abu Dhabi 17551, UAE

Received 12 December 2012; Revised 6 March 2013; Accepted 7 March 2013

Academic Editor: Roberto Barrio

Copyright © 2013 Adama Diene and Mohamed A. Salim. 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.


The permutation behavior of Dickson polynomials of the first kind has been extensively studied, while such behavior for Dickson polynomials of the second kind is less known. Necessary and sufficient conditions for a polynomial of the second kind to be a permutation over some finite fields have been established by Cohen, Matthew, and Henderson. We introduce a new way to define these polynomials and determine the number of their fixed points.