On Two Congruences Involving Apery and Franel Numbers

被引：6

作者：

Mao, Guo-Shuai ^{[1
]}

机构：

[1] Nanjing Univ Informat Sci & Technol, Dept Math, Nanjing 210044, Peoples R China

来源：

RESULTS IN MATHEMATICS | 2020年 / 75卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Congruences; Apery numbers; Franel numbers; Jacobi symbol; CONJECTURES; PROOF; SUMS; SUN;

D O I：

10.1007/s00025-020-01291-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we mainly prove a congruence conjecture of Z.-W. Sun involving Franel numbers: For any prime p > 3, we have Sigma(p-1)(k=0)(-1)(k) f(k) equivalent to (p/3) + 2p(2)/3B(p-2) (1/3) (mod p(3)), where B-n(x) is the n-th Bernoulli polynomial.

引用

页数：12

共 20 条

[1]

[Anonymous], 1972, COMBINATORIAL IDENTI

[2] ANOTHER CONGRUENCE FOR THE APERY NUMBERS [J].

BEUKERS, F .

JOURNAL OF NUMBER THEORY, 1987, 25 (02) :201-210

[3] CONGRUENCE PROPERTIES OF APERY NUMBERS [J].

CHOWLA, S ;

COWLES, J ;

COWLES, M .

JOURNAL OF NUMBER THEORY, 1980, 12 (02) :188-190

[4] SOME CONGRUENCES FOR APERY NUMBERS [J].

GESSEL, I .

JOURNAL OF NUMBER THEORY, 1982, 14 (03) :362-368

[5] Some congruences related to a congruence of Van Hamme [J].

Guo, Victor J. W. ;

Liu, Ji-Cai .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2020, 31 (03) :221-231

[6] Proof of two conjectures of Sun on congruences for Franel numbers [J].

Guo, Victor J. W. .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2013, 24 (07) :532-539

[7] Proof of some conjectures of Z.-W. Sun on congruences for Apery polynomials [J].

Guo, Victor J. W. ;

Zeng, Jiang .

JOURNAL OF NUMBER THEORY, 2012, 132 (08) :1731-1740

[8] Supercongruences for the Catalan-Larcombe-French numbers [J].

Jarvis, Frazer ;

Verrill, Helena A. .

RAMANUJAN JOURNAL, 2010, 22 (02) :171-186

[9] On two congruences involving Franel numbers [J].

Liu, Ji-Cai .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2020, 114 (04)

[10] Congruences for central binomial sums and finite polylogarithms [J].

Mattarei, Sandro ;

Tauraso, Roberto .

JOURNAL OF NUMBER THEORY, 2013, 133 (01) :131-157

← 1 2 →