Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the largest prime divisor of $n!+1$   For an integer $m >1$, we denote by $P(m)$ the largest prime divisor of $m$.
We prove that $\limsup_{n \rightarrow +\infty} P(n!+1)/n \geqslant 1+9\log
2>7.238$, which improves a result of Stewart. More generally, for any nonzero
polynomial $f(X)$ with integer coefficients, we show that $\limsup_{n
\rightarrow +\infty} P(n!+f(n))/n \geqslant 1+9\log2$. This improves a result
of Luca and Shparlinski. These improvements come from an additional
combinatoric idea to the works mentioned above.

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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin