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Azerbaijan Junior National Olympiad
2015 Azerbaijan National Olympiad
3
Azerbaijan NMO 2015
Azerbaijan NMO 2015
Source: Azerbaijan NMO 2015
October 21, 2015
algebra
polynomial
AZE JUNIOR NATIONAL MO
AZE SENIOR NATIONAL MO
Problem Statement
Find all polynomials
P
(
x
)
P(x)
P
(
x
)
with real coefficents such that
P
(
P
(
x
)
)
=
(
x
2
+
x
+
1
)
⋅
P
(
x
)
P(P(x))=(x^2+x+1)\cdot P(x)
P
(
P
(
x
))
=
(
x
2
+
x
+
1
)
⋅
P
(
x
)
where
x
∈
R
x \in \mathbb{R}
x
∈
R
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