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An arithmetic progression is a (possibly infinite) sequence of numbers such that the difference between consecutive terms is always the same value.
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Thin sets that are well-distributed over arithmetic progressions?
Sets of the form $[n^\alpha]$, $\alpha\in(1, \infty)\setminus\mathbb{N}$ are well distributed in arithmetic progressions. More generally we have that for every $\alpha\in(1, \infty)\setminus\mathbb{N} …