Let θ be a non-zero real number and let N be a positive integer. Consider the fractional parts of nθ for 0 ≤ n < N. This creates a maximum of N possible intervals. Show that there as only three possible length of this interval. I have no idea how to do this problem. It looks so simple but I am really unable to proof it. So any help will be appreciated, thanks.
2026-03-26 16:06:02.1774541162
Weyl's equidistribution theorem in the case of rational numbers
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