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Greece Contests
Greece National Olympiad
2012 Greece National Olympiad
2
2
Part of
2012 Greece National Olympiad
Problems
(1)
Polynomials
Source: Greek MO 2012 - P2
5/12/2013
Find all the non-zero polynomials
P
(
x
)
,
Q
(
x
)
P(x),Q(x)
P
(
x
)
,
Q
(
x
)
with real coefficients and the minimum degree,such that for all
x
ā
R
x \in \mathbb{R}
x
ā
R
:
P
(
x
2
)
+
Q
(
x
)
=
P
(
x
)
+
x
5
Q
(
x
)
P(x^2)+Q(x)=P(x)+x^5Q(x)
P
(
x
2
)
+
Q
(
x
)
=
P
(
x
)
+
x
5
Q
(
x
)
algebra
polynomial
algebra proposed