Geodesic
Pairs of square-free values of the type $n^2+1$, $n^2+2$
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 991-1009.

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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 number.
DOI : 10.21136/CMJ.2021.0165-20
Classification : 11L05, 11N25, 11N37
Keywords: square-free number; asymptotic formula; Kloosterman sum 
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     title = {Pairs of square-free values of the type $n^2+1$, $n^2+2$},
     journal = {Czechoslovak Mathematical Journal},
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Dimitrov, Stoyan. Pairs of square-free values of the type $n^2+1$, $n^2+2$. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 991-1009. doi : 10.21136/CMJ.2021.0165-20. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0165-20/

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