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2020 Greece National Olympiad
1
1
Part of
2020 Greece National Olympiad
Problems
(1)
P((Q(x))^3)=xP(x)(Q(x))^3 , polynomials
Source: Greek National 2020 p1 (Archimedes)
2/23/2020
Find all non constant polynomials
P
(
x
)
,
Q
(
x
)
P(x),Q(x)
P
(
x
)
,
Q
(
x
)
with real coefficients such that:
P
(
(
Q
(
x
)
)
3
)
=
x
P
(
x
)
(
Q
(
x
)
)
3
P((Q(x))^3)=xP(x)(Q(x))^3
P
((
Q
(
x
)
)
3
)
=
x
P
(
x
)
(
Q
(
x
)
)
3
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polynomial
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