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# Article

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Keywords:
integer-valued polynomial
Summary:
Let \$P\$ be a polynomial with integral coefficients. Shapiro showed that if the values of \$P\$ at infinitely many blocks of consecutive integers are of the form \$Q(m)\$, where \$Q\$ is a polynomial with integral coefficients, then \$P(x)=Q( R(x))\$ for some polynomial \$R\$. In this paper, we show that if the values of \$P\$ at finitely many blocks of consecutive integers, each greater than a provided bound, are of the form \$m^q\$ where \$q\$ is an integer greater than 1, then \$P(x)=( R(x))^q\$ for some polynomial \$R(x)\$.
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