What a Trigonometric Product!

Geometry Level 4

What is the sum of all positive integer values of \(n\) that satisfy the equation

\[ \cos\Bigl(\frac{\pi}{n}\Bigr)\cos\Bigl(\frac{2\pi}{n}\Bigr)\cos\Bigl(\frac{4\pi}{n}\Bigr)\cos\Bigl(\frac{8\pi}{n}\Bigr)\cos\Bigl(\frac{16\pi}{n}\Bigr) =\frac{1}{32}\, ? \]

×

Problem Loading...

Note Loading...

Set Loading...