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2012 Math Prize For Girls Problems
12
12
Part of
2012 Math Prize For Girls Problems
Problems
(1)
Math Prize 2012 Problem 12
Source:
9/24/2012
What is the sum of all positive integer values of
n
n
n
that satisfy the equation
cos
(
π
n
)
cos
(
2
π
n
)
cos
(
4
π
n
)
cos
(
8
π
n
)
cos
(
16
π
n
)
=
1
32
?
\cos \Bigl( \frac{\pi}{n} \Bigr) \cos \Bigl( \frac{2\pi}{n} \Bigr) \cos \Bigl( \frac{4\pi}{n} \Bigr) \cos \Bigl( \frac{8\pi}{n} \Bigr) \cos \Bigl( \frac{16\pi}{n} \Bigr) = \frac{1}{32} \, ?
cos
(
n
π
)
cos
(
n
2
π
)
cos
(
n
4
π
)
cos
(
n
8
π
)
cos
(
n
16
π
)
=
32
1
?
trigonometry