# Mystery polynomial equation in 2019.

Algebra Level 5

If the number $c$ is the largest solution of the equation $\left(x-\cos {\frac{\pi}{2020}}\right) \left(x-\cos {\frac{3\pi}{2020}}\right) \left (x-\cos {\frac{5\pi}{2020}} \right )\cdots \left( x-\cos {\frac{2019\pi}{2020}}\right) =\frac{1}{2^{1010}},$ then find the number $\left \lfloor{\frac{1}{\arccos{c}}}\right\rfloor.$

Note: The expression $\left \lfloor{\frac{1}{\arccos{c}}}\right\rfloor$ represents the floor of the number $\frac{1}{\arccos{c}}.$

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