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4
Albanian BMO TST 2009 Question 4
Albanian BMO TST 2009 Question 4
Source:
June 5, 2010
algebra
polynomial
algebra unsolved
Problem Statement
Find all the polynomials
P
(
x
)
P(x)
P
(
x
)
of a degree
≤
n
\leq n
≤
n
with real non-negative coefficients such that
P
(
x
)
⋅
P
(
1
x
)
≤
[
P
(
1
)
]
2
P(x) \cdot P(\frac{1}{x}) \leq [P(1)]^2
P
(
x
)
⋅
P
(
x
1
)
≤
[
P
(
1
)
]
2
,
∀
x
>
0
\forall x>0
∀
x
>
0
.
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