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arXiv 2205.024882022-05math.NT

$\mathbf{n^2+n+1}$ 的无平方值

Square-free values of $\mathbf{n^2+n+1}$

S. I. Dimitrov

备注：: arXiv admin note: text overlap with arXiv:2004.09975

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AI总结：

本文通过改进余项推导渐近公式，证明了形如 $n^2+n+1$ 的数中存在无穷多个无平方数。

摘要：

本文证明了形如 $n^2+n+1$ 的数中存在无穷多个无平方数。我们通过改进先前结果中的余项，推导出一个渐近公式来实现这一结论。

英文摘要：

In this paper we show that there exist infinitely many square-free numbers of the form $n^2+n+1$. We achieve this by deriving an asymptotic formula by improving the reminder term from previous results.

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