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I’m studying the correction of an exercise and I there are some points I can’t see:

In this exercise, we introduce a irrational x and function f so that f(kx)=kx-[kx] with k an integer included in the interval [0,N].

It is said that f has N+1 values (Ok) that are included in the intervals [i/N,(i+1)/N] for i integers included in [0,N-1]… I can’t see this last point. If anyone could help me understand this point…

Thanks in advance!