Square-free numbers of the form \(x^2+y^2+z^2+z+1\) and \(x^2+y^2+z+1\)
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Publication:6154115
DOI10.1134/s0001434623110494MaRDI QIDQ6154115
Publication date: 19 March 2024
Published in: Mathematical Notes (Search for Journal in Brave)
Asymptotic results on arithmetic functions (11N37) Gauss and Kloosterman sums; generalizations (11L05) Distribution of integers with specified multiplicative constraints (11N25)
Cites Work
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- A New Application of the Hardy-Littlewood-Kloosterman Method
- 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
- Pairs of square-free values of the type $n^2+1$, $n^2+2$
- Consecutive square-free numbers and square-free primitive roots
- On the consecutive square-free values of the polynomials \(x_1^2 + \cdots + x_k^2+1\), \(x_1^2 + \cdots + x_k^2+2\)
- On the $r$-free values of the polynomial $x^2 + y^2 + z^2 +k$
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