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Type: Artigo de periódico
Author: Engler, AJ
Khanduja, SK
Abstract: In this paper, all irreducible factors of bivariate polynomials of the form f(x) - g(y) over an arbitrary field are described. It also proves that the number of irreducible factors of f(x) - g(y) (counting multiplicities) does not exceed the greatest common divisor of the degrees of f(x) and g(y), yielding a well known result of Tverberg regarding the irreducibility of f(x) - g(y). It proves that if f(x) and g(y) are non-constant polynomials with coefficients in the field Q of rational numbers and deg f(x) is a prime number, then f(x) - g(y) is a product of at most two irreducible polynomials over Q. This contributes to a problem raised by Cassels which asks for the polynomials f, such that the polynomial f(x )- f(y)/x - y is reducible.
Subject: Factorization polynomials
irreducibility polynomials
special polynomials
Country: Singapura
Editor: World Scientific Publ Co Pte Ltd
Citation: International Journal Of Mathematics. World Scientific Publ Co Pte Ltd, v. 21, n. 4, n. 407, n. 418, 2010.
Rights: fechado
Identifier DOI: 10.1142/S0129167X10006082
Date Issue: 2010
Appears in Collections:Unicamp - Artigos e Outros Documentos

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