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2020 BMT Fall
23
2020 BMT Team 23
2020 BMT Team 23
Source:
January 9, 2022
trigonometry
algebra
Problem Statement
Let
0
<
θ
<
2
π
0 < \theta < 2\pi
0
<
θ
<
2
π
be a real number for which
cos
(
θ
)
+
cos
(
2
θ
)
+
cos
(
3
θ
)
+
.
.
.
+
cos
(
2020
θ
)
=
0
\cos (\theta) + \cos (2\theta) + \cos (3\theta) + ...+ \cos (2020\theta) = 0
cos
(
θ
)
+
cos
(
2
θ
)
+
cos
(
3
θ
)
+
...
+
cos
(
2020
θ
)
=
0
and
θ
=
π
n
\theta =\frac{\pi}{n}
θ
=
n
π
for some positive integer
n
n
n
. Compute the sum of the possible values of
n
≤
2020
n \le 2020
n
≤
2020
.
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