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

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  • Javier Gomez-Calderon

Abstract

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 ] .

Suggested Citation

  • Javier Gomez-Calderon, 1997. "The radical factors of f ( x ) − f ( y ) over finite fields," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:923967
    DOI: 10.1155/S0161171297001087
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