It is possible to show that $ \csc\frac{3\pi}{29}-\csc\frac{10\pi}{29}= 1.999989433...$. Prove that there are no integers $ j$, $ k$, $ n$ with odd $ n$ satisfying $ \csc\frac{j\pi}{n}-\csc\frac{k\pi}{n}= 2$.
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Tags: Irrational numbers
It is possible to show that $ \csc\frac{3\pi}{29}-\csc\frac{10\pi}{29}= 1.999989433...$. Prove that there are no integers $ j$, $ k$, $ n$ with odd $ n$ satisfying $ \csc\frac{j\pi}{n}-\csc\frac{k\pi}{n}= 2$.