Proof of Sun's conjectures on integer-valued polynomials
Number Theory
2017-02-22 v4 Combinatorics
Abstract
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 -analogues.
Cite
@article{arxiv.1601.04250,
title = {Proof of Sun's conjectures on integer-valued polynomials},
author = {Victor J. W. Guo},
journal= {arXiv preprint arXiv:1601.04250},
year = {2017}
}
Comments
12 pages, corrected a typo in Theorem 1.1