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# Sorry for all the questions lately, I have to prepare! -_-

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I think this is a trig function.

Let $$x$$ be a real number such that the five numbers $$\cos(2 \pi x)$$$$\cos(4 \pi x)$$$$\cos(8 \pi x)$$$$\cos(16 \pi x)$$, and $$\cos(32 \pi x)$$ are all nonpositive. What is the smallest possible positive value of $$x$$?

May 10, 2020