On the distribution of consecutive square-free numbers of the form [α n], [α n]+1
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alphaconsecutiveformirrationalnumbernumberssquare-freealgebraic
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In the present paper we show that there exist infinitely many consecutive square-free numbers of the form $[\alpha n]$, $[\alpha n]+1$, where $\alpha>1$ is irrational number with bounded partial quotient or irrational algebraic number.
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