# Bulgaria National Olympiad Problem 3

Algebra Level 5

Find the least natural number $$a$$ for which the equation $$\cos^2\pi(a-x)-2\cos\pi(a-x)+\cos\frac{3\pi x}{2a}\cos(\frac{\pi x}{2a}+\frac{\pi}{3})+2=0$$ has a real root.

×