Engler, A. J. ; Khanduja, Sudesh K.
(2010)
*On irreducible factors of the polynomial f(x) - g(y)*
International Journal of Mathematics, 21
(4).
pp. 407-418.
ISSN 0129-167X

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Official URL: http://www.worldscinet.com/ijm/21/2104/S0129167X10...

Related URL: http://dx.doi.org/10.1142/S0129167X10006082

## 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 degf(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-yis reducible.

Item Type: | Article |
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Source: | Copyright of this article belongs to World Scientific Publishing Company. |

Keywords: | Factorization Polynomials; Irreducibility Polynomials; Special Polynomials |

ID Code: | 83980 |

Deposited On: | 23 Feb 2012 12:26 |

Last Modified: | 23 Feb 2012 12:26 |

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