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Moldova Contests
Moldova National Olympiad
2003 Moldova National Olympiad
12.5
Special division of polynomials
Special division of polynomials
Source: Moldovan MO 2003
February 20, 2006
algebra
polynomial
algebra proposed
Problem Statement
Consider the polynomial
P
(
x
)
=
X
2
n
−
X
2
n
−
1
+
⋯
−
x
+
1
P(x)=X^{2n}-X^{2n-1}+\dots-x+1
P
(
x
)
=
X
2
n
−
X
2
n
−
1
+
⋯
−
x
+
1
, where
n
∈
N
∗
n\in{N^*}
n
∈
N
∗
. Find the remainder of the division of polynomial
P
(
x
2
n
+
1
)
P(x^{2n+1})
P
(
x
2
n
+
1
)
by
P
(
x
)
P(x)
P
(
x
)
.
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