Square-Free Numbers of the Form $$\mathbf{x^2+y^2+z^2+z+1}$$ and $$\mathbf{x^2+y^2+z+1}$$
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Published:2023-12
Issue:5-6
Volume:114
Page:1169-1183
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ISSN:0001-4346
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Container-title:Mathematical Notes
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language:en
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Short-container-title:Math Notes
Publisher
Pleiades Publishing Ltd
Reference12 articles.
1. D. I. Tolev, “On the number of pairs of positive integers $$x, y \leq H$$ such that $$x^2+y^2+1$$ is squarefree,” Monatsh. Math. 165 (3–4), 557–567 (2012).
2. G. Zhou and Y. Ding, “On the square-free values of the polynomial $$x^2+y^2+z^2+k$$,” J. Number Theory 236, 308–322 (2022).
3. G. Chen and W. Wang, “On the $$r$$-free values of the polynomial $$x^2+y^2+z^2+k$$,” Czech. Math. J. 73 (3), 955–969.
4. S. I. Dimitrov, “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,” Acta Arith. 194 (3), 281–294 (2020).
5. S. I. Dimitrov, “Pairs of square-free values of the type $$n^2+1$$, $$n^2+2$$,” Czech. Math. J. 71 (4), 991–1009 (2021).