Displaying similar documents to “On Fail-Rolle polynomials with few roots.”

Parametrization of integral values of polynomials

Giulio Peruginelli (2010)

Actes des rencontres du CIRM

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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...

Reducibility and irreducibility of Stern ( 0 , 1 ) -polynomials

Karl Dilcher, Larry Ericksen (2014)

Communications in Mathematics

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The classical Stern sequence was extended by K.B. Stolarsky and the first author to the Stern polynomials a ( n ; x ) defined by a ( 0 ; x ) = 0 , a ( 1 ; x ) = 1 , a ( 2 n ; x ) = a ( n ; x 2 ) , and a ( 2 n + 1 ; x ) = x a ( n ; x 2 ) + a ( n + 1 ; x 2 ) ; these polynomials are Newman polynomials, i.e., they have only 0 and 1 as coefficients. In this paper we prove numerous reducibility and irreducibility properties of these polynomials, and we show that cyclotomic polynomials play an important role as factors. We also prove several related results, such as the fact that a ( n ; x ) can only have simple zeros, and...