Ayache, Ahmed; Echi, Othman; Naimi, Mongi On Kronecker polynomials. (English) Zbl 1235.11013 Rocky Mt. J. Math. 41, No. 3, 707-725 (2011). Let \(n\geq 1\) be an integer. By a strong Kronecker polynomial \(P(X)\) we mean a monic polynomial with integer coefficients of degree \(n-1\) such that \(P(X)\) divides \(P(X^t)\) for each \(t\in \{1,\dots,n-1\}\). We say that \(P(X)\) is an absolutely Kronecker polynomial if \(P(X)\) divides \(P(X^t)\) for each positive integer \(t\). The aim of the authors is to describe these sets of polynomials and relate them to each other. Reviewer: Pieter Moree (Bonn) MSC: 11A41 Primes 11A51 Factorization; primality 11C08 Polynomials in number theory Keywords:Euler totient function; cyclotomic polynomial; prime number; reciprocal polynomial; roots on the unit circle PDFBibTeX XMLCite \textit{A. Ayache} et al., Rocky Mt. J. Math. 41, No. 3, 707--725 (2011; Zbl 1235.11013) Full Text: DOI References: [1] D. Caragea and V. Ene, Problems and solutions : Problems : 10802, Amer. Math. Monthly 107 (2000), 462. [2] D. Caragea, V. Ene, D. Alvis and N. Komanda, Problems and solutions : Solutions : 10802, Amer. Math. Monthly 109 (2002), 570-571. [3] P.A. Damianou, Monic polynomials in \(\mathbf Z[X]\) with roots in the unit disc , Amer. Math. Monthly 108 (2001), 253-257. · Zbl 0974.12002 [4] L. Kronecker, Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten , Crelle, Oeuvres I (1857), 105-108. [5] J.H. Nieto, On the divisibility of polynomials with integer coefficients , Divulg. Mat. 11 (2003), 149-152 (in Spanish). · Zbl 1100.13506 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.