The radical factors of f(x)−f(y) over finite fields
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 sh...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171297001087 |
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| Summary: | 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]. |
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| ISSN: | 0161-1712 1687-0425 |