# 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.

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