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On image sets of integer-valued polynomials. (English) Zbl 1239.11029
Let $$\mathrm{Int}(Z)$$ be the set of all polynomials $$f\in Q[X]$$ with $$f(Z)\subset Z$$. Two polynomials $$f,g\in \mathrm{Int}(Z)$$ are called equivalent if for some $$n\in Z$$ one has either $$f(X)=g(X-n)$$ or $$f(X)=g(-X-n)$$. The authors show that $$f,g\in \mathrm{Int}(Z)$$ satisfy $$f(Z)=g(Z)$$ if and only if they are either equivalent, or for some odd $$k$$ one has $$f(-X)=f(X-k)$$ and $$g$$ is equivalent to $$f(2X)$$.

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