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

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

2011-12-24

arxiv.org/abs/1112.5753v1

Mathematics

Rings and Algebras

9 pages

Scientific paper

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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