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4
IMC 2020 Problem 4
IMC 2020 Problem 4
Source: IMC 2020
July 27, 2020
IMC
Polynomials
algebra
polynomial
college contests
IMC 2020
Problem Statement
A polynomial
p
p
p
with real coefficients satisfies
p
(
x
+
1
)
−
p
(
x
)
=
x
100
p(x+1)-p(x)=x^{100}
p
(
x
+
1
)
−
p
(
x
)
=
x
100
for all
x
∈
R
.
x \in \mathbb{R}.
x
∈
R
.
Prove that
p
(
1
−
t
)
≥
p
(
t
)
p(1-t) \ge p(t)
p
(
1
−
t
)
≥
p
(
t
)
for
0
≤
t
≤
1
/
2.
0 \le t \le 1/2.
0
≤
t
≤
1/2.
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