Lengths of factorizations of integer-valued polynomials on Krull domains with prime elements (Q6586474)

For an integral domain \(R\) with fraction field \(K\) denote by Int\((R)\) the ring of integer-valued polynomials of \(R\), i.e. the ring of polynomials over \(K\) with \(f(R)\subset R\). It has been shown by \textit{S. Frisch} [Monatsh. Math. 171, No. 3--4, 341--350 (2013; Zbl 1282.13004)] that if \(k\) and \(n_1,n_2,\dots,n_k\) are given integers \(\ge2\), then there is a polynomial \(f(X)\in Int(Z)\) having \(k\) distinct factorizations into irreducibles of lengths \(n_1,n_2,\dots,n_k\). Later \textit{S. Frisch} et al. [J. Algebra 528, 231--249 (2019; Zbl 1419.13002)] established the same assertion for Int\((R)\) in the case when \(R\) is a Dedekind domain having infinitely many prime ideals with finite residue fields, and \textit{V. Fadinger-Held} et al. [Monatsh. Math. 202, No. 4, 773--789 (2023; Zbl 1544.11092)] did this when \(R\) is a valuation ring of a global field.\N\NIn the paper under review, the authors show that this assertion holds when \(R\) is a Krull domain having a prime ideal with finite residue field.