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arXiv · 1112.5753

A construction of integer-valued polynomials with prescribed sets of lengths of factorizations

Sophie Frisch
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Abstract

For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a product of n irreducibles in Int(Z)={g in Q[x] | g(Z) contained in Z}.

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Sophie Frisch. 2011-12-24. A construction of integer-valued polynomials with prescribed sets of lengths of factorizations. https://doi.org/10.1007/s00605-013-0508-z

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