Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof of Sun's conjectures on integer-valued polynomials   Recently, Z.-W. Sun introduced two kinds of polynomials related to the
Delannoy numbers, and proved some supercongruences on sums involving those
polynomials. We deduce new summation formulas for squares of those polynomials
and use them to prove that certain rational sums involving even powers of those
polynomials are integers whenever they are evaluated at integers. This confirms
two conjectures of Z.-W. Sun. We also conjecture that many of these results
have neat $q$-analogues.

24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio