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MathNet 2011 Question 79

Math Olympiad Vault · MathNet 2011

Question 79

Solve the equation:
$$
\cos \pi x = \left[ \frac{x}{2} - \left[ \frac{x}{2} \right] - \frac{1}{2} \right].
$$

Here $[a]$ stands for the greatest integer number that does not exceed $a$.