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Schoenemann's Theorem

If the integral Coefficients $C_0$, $C_1$, ..., $C_{N-1}$ of the Polynomial


are divisible by a Prime Number $p$, while the free term $C_0$ is not divisible by $p^2$, then $f(x)$ is irreducible in the natural rationality domain.

See also Abel's Irreducibility Theorem, Abel's Lemma, Gauss's Polynomial Theorem, Kronecker's Polynomial Theorem


Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, p. 118, 1965.

© 1996-9 Eric W. Weisstein