Actes des rencontres du CIRM

We will recall a recent result about the classification of those polynomial in one variable with rational coefficients whose image over the integer is equal to the image of an integer coefficients polynomial in possibly many variables. These set is polynomially generated over the integers by a family of polynomials whose denominator is $2$ and they have a symmetry with respect to a particular axis.

We will also give a description of the linear factors of the bivariate separated polynomial $f\left(X\right)-f\left(Y\right)$ over a number field $K$, which we need to formulate a conjecture for a generalization of the previous result over a generic number field.

Published online : 2011-10-20
DOI : https://doi.org/10.5802/acirm.32
Classification:  11D85,  11C08,  13F20
Keywords: Integer-valued polynomial, image of a polynomial, linear factor bivariate separated polynomial.

@article{ACIRM_2010__2_2_41_0,
     author = {Giulio Peruginelli},
     title = {Parametrization of integral values of polynomials},
     journal = {Actes des rencontres du CIRM},
     publisher = {CIRM},
     volume = {2},
     number = {2},
     year = {2010},
     pages = {41-49},
     doi = {10.5802/acirm.32},
     language = {en},
     url = {https://acirm.centre-mersenne.org/item/ACIRM_2010__2_2_41_0}
}

Peruginelli, Giulio. Parametrization of integral values of polynomials. Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 41-49. doi : 10.5802/acirm.32. https://acirm.centre-mersenne.org/item/ACIRM_2010__2_2_41_0/