# A. Cohn's irreducibility criterion

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\begin{theorem}
Assume $n \geq 2$ is an integer  and that $P$ is a polynomial with coefficients in $\{0,1,\ldots,n-1\}$. If $P(n)$ is prime then $P(x)$ is \PMlinkname{irreducible}{IrreduciblePolynomial2} in $\mathbb{Z}[x]$.
\end{theorem}
A proof is given in \cite{MRM}.

A. Cohn \cite{PZ} proved this theorem for the case $n=10$.

This special case of the above theorem is sketched as problem 128, Part VIII, in \cite{PZ}.

\begin{thebibliography}{0}
\bibitem[PZ]{PZ}
George PÃ³lya, Gabor Szego,
{\it Problems and Theorems in Analysis II},
Classics in Mathematics 1998.
\bibitem[MRM]{MRM}
M. Ram Murty, {\it Prime Numbers and Irreducible Polynomials}, American
Mathematical Monthly, vol. 109, (2002), 452-458.
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