Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential Sums and Congruences with Factorials   We estimate the number of solutions of certain diagonal congruences involving
factorials. We use these results to bound exponential sums with products of two
factorials $n!m!$ and also derive asymptotic formulas for the number of
solutions of various congruences with factorials. For example, we prove that
the products of two factorials $n!m!$ with $\max\{n,m\}<p^{1/2+\epsilon}$ are
uniformly distributed modulo $p$, and that any residue class modulo $p$ is
representable in the form $m!n!+n_1! + ... +n_{49}!$ with $\max \{m,n, n_1,
>..., n_{49}\} < p^{8775/8794+ \epsilon}$.

19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
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The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin