## Determining integer-valued polynomials from their image.(English)Zbl 1439.13047

Summary: This note summarizes a presentation made at the Third International Meeting on Integer Valued Polynomials and Problems in Commutative Algebra. All the work behind it is joint with S. T. Chapman, and appeared in [J. Algebra 348, No. 1, 350–353 (2011; Zbl 1239.11029)]. Let $$\operatorname{Int}(\mathbb Z)$$ represent the ring of polynomials with rational coefficients which are integer-valued at integers. We determine criteria for two such polynomials to have the same image set on $$\mathbb Z$$.

### MSC:

 13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations 11C08 Polynomials in number theory 13F20 Polynomial rings and ideals; rings of integer-valued polynomials 13G05 Integral domains 13B25 Polynomials over commutative rings

### Keywords:

integer-valued polynomial

Zbl 1239.11029
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### References:

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