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P(x) Polynomial - Iran NMO 2001 (Second Round) - Problem4
P(x) Polynomial - Iran NMO 2001 (Second Round) - Problem4
Source:
October 4, 2010
algebra
polynomial
algebra proposed
Problem Statement
Find all polynomials
P
P
P
with real coefficients such that
∀
x
∈
R
\forall{x\in\mathbb{R}}
∀
x
∈
R
we have:
P
(
2
P
(
x
)
)
=
2
P
(
P
(
x
)
)
+
2
(
P
(
x
)
)
2
.
P(2P(x))=2P(P(x))+2(P(x))^2.
P
(
2
P
(
x
))
=
2
P
(
P
(
x
))
+
2
(
P
(
x
)
)
2
.
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