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2
Polynomial equation - BxMO 2010
Polynomial equation - BxMO 2010
Source:
May 2, 2010
algebra
polynomial
functional equation
algebra proposed
Problem Statement
Find all polynomials
p
(
x
)
p(x)
p
(
x
)
with real coe ffcients such that
p
(
a
+
b
−
2
c
)
+
p
(
b
+
c
−
2
a
)
+
p
(
c
+
a
−
2
b
)
=
3
p
(
a
−
b
)
+
3
p
(
b
−
c
)
+
3
p
(
c
−
a
)
p(a + b - 2c) + p(b + c - 2a) + p(c + a - 2b) = 3p(a - b) + 3p(b - c) + 3p(c - a)
p
(
a
+
b
−
2
c
)
+
p
(
b
+
c
−
2
a
)
+
p
(
c
+
a
−
2
b
)
=
3
p
(
a
−
b
)
+
3
p
(
b
−
c
)
+
3
p
(
c
−
a
)
for all
a
,
b
,
c
∈
R
a, b, c\in\mathbb{R}
a
,
b
,
c
∈
R
.(2nd Benelux Mathematical Olympiad 2010, Problem 2)
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