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Values of Polynomials over Integral Domains

Steven H.Weintraub
The American Mathematical Monthly
Vol. 121, No. 1 (January 2014), pp. 73-74
DOI: 10.4169/amer.math.monthly.121.01.073
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Page Count: 2
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Abstract It is well known that no nonconstant polynomial with integer coefficients can take on only prime values. We isolate the property of the integers that accounts for this, and give several examples of integral domains for which there are polynomials that only take on unit or prime values.

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