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Iran MO (3rd Round)
2015 Iran MO (3rd round)
4
Constant polynomial
Constant polynomial
Source: Iranian third round algebra 2015 problem 4
September 8, 2015
algebra
polynomial
complex numbers
Problem Statement
p
(
x
)
∈
C
[
x
]
p(x)\in \mathbb{C}[x]
p
(
x
)
∈
C
[
x
]
is a polynomial such that:
∀
z
∈
C
,
∣
z
∣
=
1
⟹
p
(
z
)
∈
R
\forall z\in \mathbb{C}, |z|=1\Longrightarrow p(z)\in \mathbb{R}
∀
z
∈
C
,
∣
z
∣
=
1
⟹
p
(
z
)
∈
R
Prove that
p
(
x
)
p(x)
p
(
x
)
is constant.
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