|Autors: Dimitrov, S. I.|
Title: Consecutive square-free values of the form [αp], [αp] + 1
Keywords: Consecutive square-free numbers, Asymptotic formula
Abstract: In this short paper we shall prove that there exist infinitely many consecutive square-free numbers of the form [αp], [αp] + 1, where p is prime and α>0 is irrational algebraic number. We also establish an asymptotic formula for the number of such square-free pairs when p does not exceed given sufficiently large positive integer.
Copyright Proc. Jangjeon Math. Soc.
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