[Trigonometric Equations]

Solve the equation:

$$
\cos \pi \frac{x}{31} \cos 2 \pi \frac{x}{31} \cos 4 \pi \frac{x}{31} \cos 8 \pi \frac{x}{31} \cos 16 \pi \frac{x}{31}=\frac{1}{32}
$$
Multiply the equation by $32 \sin \frac{\pi x}{31}$.

## Answer

$x_{1}=2 n, n \neq 31 l ; x_{2}=\frac{31}{33}(2 n+1), n \neq 33 l+16(n, l \in \mathbb{Z})$.