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International Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 4, Pages 799-802

The radical factors of f(x)f(y) over finite fields

Department of Mathematics, New Kensington Campus, The Pennsylvania State University, New Kensington 15068, PA, USA

Received 6 October 1995; Revised 23 April 1996

Copyright © 1997 Hindawi Publishing Corporation. 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.


Let F denote the finite field of order q For f(x) in F[x], let f*(x,y) denote the substitution polynomial f(x)f(y). The polynomial f*(x,y) has frequently been used in questions on the values set of f(x) In this paper we consider the irreducible factors of f*(x,y) that are “solvable by radicals” We show that if R(x,y) denotes the product of all the irreducible factors of f*(x,y) that are solvable by radicals, then R(x,y)=g(x)g(y) and f(x)=G(g(x)) for some polynomials g(x) and G(x) in F[x].