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Miklós Schweitzer
2016 Miklós Schweitzer
3
3
Part of
2016 Miklós Schweitzer
Problems
(1)
Hensel's lemma for polynomial rings
Source: Miklós Schweitzer 2016, Problem 3
11/2/2016
Prove that for any polynomial
P
P
P
with real coefficients, and for any positive integer
n
n
n
, there exists a polynomial
Q
Q
Q
with real coefficients such that
P
(
x
)
2
+
Q
(
x
)
2
P(x)^2 +Q(x)^2
P
(
x
)
2
+
Q
(
x
)
2
is divisible by
(
1
+
x
2
)
n
(1+x^2)^n
(
1
+
x
2
)
n
.
algebra
polynomial
Ring Theory
Field theory
Miklos Schweitzer