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4
Inequality of a polynomial
Inequality of a polynomial
Source:
April 19, 2013
inequalities
algebra
polynomial
Problem Statement
A polynomial
p
p
p
with integer coefficients is such that
p
(
−
n
)
<
p
(
n
)
<
n
p(-n) < p(n) < n
p
(
−
n
)
<
p
(
n
)
<
n
for some integer
n
n
n
. Prove that
p
(
−
n
)
<
−
n
p(-n) < -n
p
(
−
n
)
<
−
n
.
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