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Polynomial problem
Polynomial problem
Source: Greek TST 2014-Pr.2.
June 23, 2014
algebra
polynomial
algebra proposed
Problem Statement
Find all real non-zero polynomials satisfying
P
(
x
)
3
+
3
P
(
x
)
2
=
P
(
x
3
)
−
3
P
(
−
x
)
P(x)^3+3P(x)^2=P(x^{3})-3P(-x)
P
(
x
)
3
+
3
P
(
x
)
2
=
P
(
x
3
)
−
3
P
(
−
x
)
for all
x
∈
R
x\in\mathbb{R}
x
∈
R
.
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