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3
Composition is square implies polynomial is square
Composition is square implies polynomial is square
Source: Kürschák 2016, problem 3
October 7, 2016
algebra
polynomial
Problem Statement
If
p
,
q
∈
R
[
x
]
p,q\in\mathbb{R}[x]
p
,
q
∈
R
[
x
]
satisfy
p
(
p
(
x
)
)
=
q
(
x
)
2
p(p(x))=q(x)^2
p
(
p
(
x
))
=
q
(
x
)
2
, does it follow that
p
(
x
)
=
r
(
x
)
2
p(x)=r(x)^2
p
(
x
)
=
r
(
x
)
2
for some
r
∈
R
[
x
]
r\in\mathbb{R}[x]
r
∈
R
[
x
]
?
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