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标题：The radical factors of <mml:math alttext="$f\left( x \right) - f\left( y \right)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> over finite fields
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作者：Javier Gomez-Calderon
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1997
卷号：20
DOI：10.1155/S0161171297001087
出版社：Hindawi Publishing Corporation
摘要：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].