Czechoslovak Mathematical Journal, Vol. 71, No. 4, pp. 991-1009, 2021
Pairs of square-free values of the type $n^2+1$, $n^2+2$
Stoyan Dimitrov
Received April 26, 2020. Published online June 17, 2021.
Abstract: 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.
Keywords: square-free number; asymptotic formula; Kloosterman sum
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