Difference between revisions of "Schonemann's criterion"
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− | For a polynomial q denote by <math>q^*</math> the residue of <math>q</math> modulo <math>p</math>. | + | For a polynomial <math>q</math> denote by <math>q^*</math> the residue of <math>q</math> modulo <math>p</math>. |
Suppose the following conditions hold: | Suppose the following conditions hold: | ||
* <math>k=f^n+pg</math> with <math>n\geq 1</math>, <math>p</math> prime, and <math>f,g\in \mathbb{Z}[X]</math>. | * <math>k=f^n+pg</math> with <math>n\geq 1</math>, <math>p</math> prime, and <math>f,g\in \mathbb{Z}[X]</math>. |
Revision as of 14:07, 21 October 2012
For a polynomial denote by
the residue of
modulo
.
Suppose the following conditions hold:
with
,
prime, and
.
.
is primitive.
is irreducible in
.
does not divide
.
Then is irreducible in
.
See also Eisenstein's criterion.