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Greece Contests
Greece National Olympiad
2005 Greece National Olympiad
1
Easy polynomial
Easy polynomial
Source: Greece
November 5, 2005
algebra
polynomial
system of equations
algebra proposed
Problem Statement
Find the polynomial
P
(
x
)
P(x)
P
(
x
)
with real coefficients such that
P
(
2
)
=
12
P(2)=12
P
(
2
)
=
12
and
P
(
x
2
)
=
x
2
(
x
2
+
1
)
P
(
x
)
P(x^2)=x^2(x^2+1)P(x)
P
(
x
2
)
=
x
2
(
x
2
+
1
)
P
(
x
)
for each
x
ā
R
x\in\mathbb{R}
x
ā
R
.
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