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Austrian-Polish
2006 Austrian-Polish Competition
2
2
Part of
2006 Austrian-Polish Competition
Problems
(1)
Find Polynomials
Source: Austrian-Polish 2006 Problem2
8/21/2006
Find all polynomials
P
(
x
)
P(x)
P
(
x
)
with real coefficients satisfying the equation
(
x
+
1
)
3
P
(
x
−
1
)
−
(
x
−
1
)
3
P
(
x
+
1
)
=
4
(
x
2
−
1
)
P
(
x
)
(x+1)^{3}P(x-1)-(x-1)^{3}P(x+1)=4(x^{2}-1) P(x)
(
x
+
1
)
3
P
(
x
−
1
)
−
(
x
−
1
)
3
P
(
x
+
1
)
=
4
(
x
2
−
1
)
P
(
x
)
for all real numbers
x
x
x
.
algebra
polynomial
algebra unsolved