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2021 Chile National Olympiad
3
4p(x^2) = 4(p(x))^2 + 4p(x)- 1
4p(x^2) = 4(p(x))^2 + 4p(x)- 1
Source: 2021 Chile National Olympiad level 2 p3
October 22, 2022
polynomial
algebra
Problem Statement
Find all polynomials
p
(
x
)
p(x)
p
(
x
)
with real coefficients that satisfy
4
p
(
x
2
)
=
4
(
p
(
x
)
)
2
+
4
p
(
x
)
ā
1
4p(x^2) = 4(p(x))^2 + 4p(x)- 1
4
p
(
x
2
)
=
4
(
p
(
x
)
)
2
+
4
p
(
x
)
ā
1
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