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Search: All articles in the CMB digital archive with keyword irreducible polynomial

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1. CMB Online first

Dubickas, Artūras
 Linear Forms in Monic Integer Polynomials We prove a necessary and sufficient condition on the list of nonzero integers $u_1,\dots,u_k$, $k \geq 2$, under which a monic polynomial $f \in \mathbb{Z}[x]$ is expressible by a linear form $u_1f_1+\dots+u_kf_k$ in monic polynomials $f_1,\dots,f_k \in \mathbb{Z}[x]$. This condition is independent of $f$. We also show that if this condition holds, then the monic polynomials $f_1,\dots,f_k$ can be chosen to be irreducible in $\mathbb{Z}[x]$. Keywords:irreducible polynomial, height, linear form in polynomials, Eisenstein's criterionCategories:11R09, 11C08, 11B83

2. CMB 2009 (vol 52 pp. 511)

Bonciocat, Anca Iuliana; Bonciocat, Nicolae Ciprian
 The Irreducibility of Polynomials That Have One Large Coefficient and Take a Prime Value We use some classical estimates for polynomial roots to provide several irreducibility criteria for polynomials with integer coefficients that have one sufficiently large coefficient and take a prime value. Keywords:Estimates for polynomial roots, irreducible polynomialsCategories:11C08, 11R09

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