Theorem 4.1
(Hensel’s Lemma version 1)
.
Assuming that:
(
K
,
|
∙
|
)
is a complete
discretely valued field
f
(
X
)
∈
O
K
[
X
]
assume
∃
a
∈
O
K
such that
|
f
(
a
)
|
<
|
f
′
(
a
)
|
2
Then
there exists a unique
x
∈
O
K
such that
f
(
x
)
=
0
and
|
x
−
a
|
<
|
f
′
(
a
)
|
.