Proof of Sun's conjectures on integer-valued polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

Guo, Victor J. W.¹ 

[1] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Jiangsu, Peoples R China

关键词: Delannoy number;    q-Delannoy numbers;    q-Binomial coefficients;    Zeilberger algorithm;   

DOI  :  10.1016/j.jmaa.2016.06.028

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free