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Problem 2
Polynomial equation
Polynomial equation
Source: Swiss IMO TST 2016. Problem 2
July 27, 2017
algebra
polynomial
function
Problem Statement
Find all polynomial functions with real coefficients for which
(
x
−
2
)
P
(
x
+
2
)
+
(
x
+
2
)
P
(
x
−
2
)
=
2
x
P
(
x
)
(x-2)P(x+2)+(x+2)P(x-2)=2xP(x)
(
x
−
2
)
P
(
x
+
2
)
+
(
x
+
2
)
P
(
x
−
2
)
=
2
x
P
(
x
)
for all real
x
x
x
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