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National and Regional Contests
India Contests
India LIMIT
2020 LIMIT
2020 LIMIT Category 1
1
LIMIT 2020 P1
LIMIT 2020 P1
Source: LIMIT 2020
April 11, 2020
algebra
polynomial
Problem Statement
Find all polynomial
P
(
x
)
P(x)
P
(
x
)
with degree
≤
n
\leq n
≤
n
and non negative coefficients such that
P
(
x
)
P
(
1
x
)
≤
P
(
1
)
2
P(x)P(\frac{1}{x})\leq P(1)^2
P
(
x
)
P
(
x
1
)
≤
P
(
1
)
2
for all positive
x
x
x
. Here
n
n
n
is a natuaral number
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