Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof of some congruence conjectures of Z.-H. Sun involving
  Ap\'{e}ry-like numbers   In this paper, we mainly prove the following conjecture of Z.-H. Sun
cite{SH20}: Let $p>3$ be a prime. Then
$$\sum_{k=0}^{p-1}\binom{2k}k\frac{3k+1}{(-16)^k}f_k\equiv(-1)^{(p-1)/2}p+p^3E_{p-3}\pmod{p^4},$$
where $f_n=\sum_{k=0}^n\binom{n}k^3$ and $E_n$ stand for the $n$th Franel
number and $n$th Euler number respectively.

20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat