Some congruences related to the q-Ferniat quotients

被引:3
作者
Guo, Victor J. W. [1 ]
机构
[1] E China Normal Univ, Dept Math, Shanghai Key Lab PMMP, Shanghai 200241, Peoples R China
基金
中国国家自然科学基金;
关键词
Fermat quotients; q-Fermat quotients; Glaisher's congruence; Kohnen's congruence; q-Delannoy numbers; Dilcher's identity; Q-IDENTITIES; ARITHMETIC THEORY; HARMONIC NUMBERS; Q-ANALOGS;
D O I
10.1142/S1793042115500554
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We give q-analogues of the following congruences by Z.-W. Sun: Sigma(p-1)(k=1) D-k/k equivalent to - 2(p-1)-1/p (mod p), Sigma(p-1)(k=1) H-k/k2(k) equivalent to 0 (mod p), p >= 5, where p is an odd prime, D-n = Sigma(n)(k=0) ((2k)(n+k)) ((2k)(k)) are the Delannoy numbers, and H-n = Sigma(n)(k=1) 1/k are the harmonic numbers. We also prove that, for any positive integer m and prime p > m + 1, Sigma(1 <= k1 <=...<= km <= p-1) 1/k(1)...k(m)2(km) equivalent to 1/2 Sigma(p-1)(k=1) (-1)(k-1)/k(m) (mod p), which is a multiple generalization of Kohnen's congruence. Furthermore, a q-analogue of this congruence is established.
引用
收藏
页码:1049 / 1060
页数:12
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