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Find all positive integer values of  that satisfy the equation

\(cos(\pi/n)cos(2\pi/n)cos(4\pi/n)cos(8\pi/n)cos(16\pi/n) = 1/32\)
Enter all the solutions, separated by commas.

 Apr 13, 2020
 #1
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+1

Since there are 5 factors and the product is 1/32, find the fiftth root of 1/32, which is 1/2.

 

Solve:  cos( pi / n )  =  0.50

--->   pi / n  =  cos-1(0.50)

--->        pi  =  n · cos-1(0.50)

--->        n  =  pi / cos-1(0.50)

--->        n  =  3

 

Each of the other factors have a value of -0.50.

 Apr 13, 2020

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