Consecutive square-free numbers of a special form
classification
🧮 math.NT
keywords
consecutiveformnumberssquare-freeasymptoticestablishexistfixed
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In the present paper we prove that for any fixed $1<c<7/6$ there exist infinitely many consecutive square-free numbers of the form $[n^c], [n^c]+1$ and we also establish an asymptotic formula in given interval.
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