Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof of Sun's conjectures on super congruences and the divisibility of
  certain binomial sums   In this paper, we prove two conjectures of Z.-W. Sun:
$$2n\binom{2n}n\big|\sum_{k=0}^{n-1}(3k+1)\binom{2k}k^3{16}^{n-1-k}\
\mbox{for}\ \mbox{all}\ n=2,3,\cdots,$$ and
$$\sum_{k=0}^{(p-1)/2}\frac{3k+1}{16^k}\binom{2k}{k}^3\equiv
p+2\left(\frac{-1}{p}\right)p^3E_{p-3}\pmod{p^4},$$ where $p>3$ is a prime and
$E_0,E_1,E_2,\cdots$ are Euler numbers.

31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn