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Romania Team Selection Test
1990 Romania Team Selection Test
3
2P(2x^2 -1) = P(x)^2 -1
2P(2x^2 -1) = P(x)^2 -1
Source: Romania IMO TST 1990 p3
February 19, 2020
polynomial
algebra
functional
functional equation
Problem Statement
Find all polynomials
P
(
x
)
P(x)
P
(
x
)
such that
2
P
(
2
x
2
−
1
)
=
P
(
x
)
2
−
1
2P(2x^2 -1) = P(x)^2 -1
2
P
(
2
x
2
−
1
)
=
P
(
x
)
2
−
1
for all
x
x
x
.
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