Pairs of square-free values of the type $n^2+1$, $n^2+2$

DOI10.21136/CMJ.2021.0165-20MaRDI QIDQ5016069

Stoyan Ivanov Dimitrov

Publication date: 10 December 2021

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.09975

zbMATH Keywords

Kloosterman sumasymptotic formulasquare-free number

Mathematics Subject Classification ID

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

Related Items (4)

Counting square-free integers represented by binary quadratic forms of a fixed discriminant ⋮ On the consecutive square-free values of the polynomials \(x_1^2 + \cdots + x_k^2+1\), \(x_1^2 + \cdots + x_k^2+2\) ⋮ Square-free numbers of the form \(x^2+y^2+z^2+z+1\) and \(x^2+y^2+z+1\) ⋮ Consecutive square-free values of the type $x^2+y^2+z^2+k$, $x^2+y^2+z^2+k+1$

Cites Work

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• The square sieve and consecutive square-free numbers
• Einige Sätze über quadratfreie Zahlen
• Square-free values of n²+1
• On the number of pairs of positive integers $x, y \leq H$ such that $x^2+y^2+1$, $x^2+y^2+2$ are square-free
• ON THE EXPONENTIAL SUM WITH SQUARE-FREE NUMBERS
• On the distribution of consecutive square-free numbers of the form $\mathbf{[\alpha n, [\alpha n]+1}$]
• CONSECUTIVE SQUARE-FREE NUMBERS OF THE FORM [nc, [nc] + 1]
• Consecutive square-free values of the form $\mathbf{[\alpha p, [\alpha p]+1}$]

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