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Putnam
1985 Putnam
A5
Putnam 1985 A5
Putnam 1985 A5
Source:
August 5, 2019
Putnam
Problem Statement
Let
I
m
=
∫
0
2
π
cos
(
x
)
cos
(
2
x
)
⋯
cos
(
m
x
)
d
x
.
I_{m}=\textstyle\int_{0}^{2 \pi} \cos (x) \cos (2 x) \cdots \cos (m x) d x .
I
m
=
∫
0
2
π
cos
(
x
)
cos
(
2
x
)
⋯
cos
(
m
x
)
d
x
.
For which integers
m
,
1
≤
m
≤
10
m, 1 \leq m \leq 10
m
,
1
≤
m
≤
10
is
I
m
≠
0
?
I_{m} \neq 0 ?
I
m
=
0
?
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