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Moldova Contests
Moldova National Olympiad
2007 Moldova National Olympiad
12.1
Polynomial divisibility
Polynomial divisibility
Source: Moldova MO 2007 12th grade day I problem 1
March 3, 2007
algebra
polynomial
algebra proposed
Problem Statement
For
a
∈
C
∗
a\in C^{*}
a
∈
C
∗
find all
n
∈
N
n\in N
n
∈
N
such that
X
2
(
X
2
−
a
X
+
a
2
)
2
X^{2}(X^{2}-aX+a^{2})^{2}
X
2
(
X
2
−
a
X
+
a
2
)
2
divides
(
X
2
+
a
2
)
n
−
X
2
n
−
a
2
n
(X^{2}+a^{2})^{n}-X^{2n}-a^{2n}
(
X
2
+
a
2
)
n
−
X
2
n
−
a
2
n
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