Ostrowski's criterion
Revision as of 11:23, 15 June 2021 by Tigerzhang (talk | contribs)
Ostrowski's Criterion states that:
Let . If
is a prime and
then
is irreducible.
Proof
Let be a root of
. If
, then
a contradiction. Therefore,
.
Suppose . Since
, one of
and
is 1. WLOG, assume
. Then, let
be the leading coefficient of
. If
are the roots of
, then
. This is a contradiction, so
is irreducible.
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