A note on some relations among special sums of reciprocals modulo p

被引：4
|
作者：
Skula, Ladislav [1 ]
机构：
[1] Univ Technol, Fac Math Engn, CZ-61669 Brno, Czech Republic
来源：
MATHEMATICA SLOVACA | 2008年 / 58卷 / 01期
关键词：
sum of reciprocals modulo p; Fermat quotient; Fibonacci quotient;
D O I：
10.2478/s12175-007-0050-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note the sums s(k,N) of reciprocals [GRAPHICS] are investigated, where p is an odd prime, N, k are integers, p does not divide N, N >= 1 and 0 <= k <= N - 1. Some linear relations for these sums are derived using "logarithmic property" and Lerch's Theorem on the Fermat quotient. Particularly in case N = 10 another linear relation is shown by means of Williams' congruences for the Fibonacci numbers. (c) 2008 Mathematical Institute Slovak Academy of Sciences.
引用
收藏
页码：5 / 10
页数：6
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