Proof of some conjectures of Z.-W. Sun on congruences for Apery polynomials

被引：25

作者：

Guo, Victor J. W. ^{[1
]}

Zeng, Jiang ^{[2
]}

机构：

[1] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China

[2] Univ Lyon 1, Inst Camille Jordan, CNRS, UMR 5208, F-69622 Villeurbanne, France

来源：

JOURNAL OF NUMBER THEORY | 2012年 / 132卷 / 08期

基金：

美国国家科学基金会;

关键词：

Apery polynomials; Pfaff-Saalschutz identity; Legendre symbol; Schmidt numbers; Schmidt polynomials;

D O I：

10.1016/j.jnt.2012.02.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Apery polynomials are defined by A(n)(x) = Sigma(n)(k=0) (n k)(2) (n+k k)(2) x(k) for all nonnegative integers n. We confirm several conjectures of Z.-W. Sun on the congruences for the sum Sigma(n-1)(k=0)(-1)(k)(2k+1)A(k)(x) with x is an element of Z. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1731 / 1740

页数：10

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