Consecutive square-free values of the type $x^{2}+y^{2}+z^{2}+k$, $x^{2}+y^{2}+z^{2}+k+1$
| Autor: | Feng, Ya-Fang |
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| Jazyk: | angličtina |
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| Druh dokumentu: | Non-fiction |
| Abstrakt: | Abstract: We show that for any given integer $k$ there exist infinitely many consecutive square-free numbers of the type $x^{2}+y^{2}+z^{2}+k$, $x^{2}+y^{2}+z^{2}+k+1$. We also establish an asymptotic formula for $1\leq x, y, z \leq H$ such that $x^{2}+y^{2}+z^{2}+k$, $x^{2}+y^{2}+z^{2}+k+1$ are square-free. The method we used in this paper is due to Tolev. |
| Databáze: | Katalog Knihovny AV ČR |
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