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On Kronecker polynomials. (English) Zbl 1235.11013

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.

MSC:

11A41 Primes
11A51 Factorization; primality
11C08 Polynomials in number theory
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References:

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