Pairs of square-free values of the type $\mathbf{n^2+1}$, $\mathbf{n^2+2}$

DOI10.21136/CMJ.2021.0165-20arXiv2004.09975MaRDI QIDQ6339146

Stoyan Ivanov Dimitrov

Publication date: 21 April 2020

Abstract: In the present paper we show that there exist infinitely many consecutive square-free numbers of the form $n^2+1$, $n^2+2$. We also establish an asymptotic formula for the number of such square-free pairs when $n$ does not exceed given sufficiently large positive integer.

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Gauss and Kloosterman sums; generalizations (11L05) Distribution of integers with specified multiplicative constraints (11N25)

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