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Baltic Way
2005 Baltic Way
4
4
Part of
2005 Baltic Way
Problems
(1)
Find three polynomials
Source: Baltic Way 2005/4
11/7/2005
Find three different polynomials
P
(
x
)
P(x)
P
(
x
)
with real coefficients such that
P
(
x
2
+
1
)
=
P
(
x
)
2
+
1
P\left(x^2 + 1\right) = P(x)^2 + 1
P
(
x
2
+
1
)
=
P
(
x
)
2
+
1
for all real
x
x
x
.
algebra
polynomial
algebra proposed