Proof of some congruences conjectured by Z.-W. Sun

被引：7
|
作者：
Mao, Guo-Shuai [1 ]
机构：
[1] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2017年 / 13卷 / 08期
关键词：
Central binomial coefficients; Franel numbers; harmonic numbers; NUMBERS;
D O I：
10.1142/S1793042117501068
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we show that for any prime p > 3, S-k=1(p-1) (-1)(k)f(k)h(k)/k equivalent to 1/2 (p/3) Bp-2 (1/3) (mod p) and S-k=1(p-1) g(k)H(k)/k equivalent to - 1/2 (p/3) Bp-2 (1/3) (mod p), where Bn(x) denotes the Bernoulli polynomial of degree n. And we prove that S-k=1(p-1) ((2k)(k))H-k/k(2)4(k) equivalent to 3/2 Bp-3 (mod p) and S-k=1(p-1) ((2k)(k))H-k/k(2)4(k) equivalent to 7/6pB(p-3) (mod p(2)), where Bn stands for the nth Bernoulli number. This confirms several conjectures of Z.-W. Sun.
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页码：1983 / 1993
页数：11
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