Skula, Ladislav A note on some relations among special sums of reciprocals modulo \(p\). (English) Zbl 1164.11001 Math. Slovaca 58, No. 1, 5-10 (2008). In this note the sums \(s(k,N)\) of reciprocals \(\sum \limits _{\frac {kp}{N}< x <\frac {(k+1)p}{N}}\frac {1}{x} \pmod p\) are investigated, where \(p\) is an odd prime, \(N\), \(k\) are integers, \(p\) does not divide \(N,N\geq 1\) and \(0\leq k\leq N-1\). 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 William’s congruences for the Fibonacci numbers. Reviewer: Stanislav Jakubec (Bratislava) Cited in 1 ReviewCited in 4 Documents MSC: 11A07 Congruences; primitive roots; residue systems 11B39 Fibonacci and Lucas numbers and polynomials and generalizations Keywords:sum of reciprocals modulo \(p\); Fermat quotient; Fibonacci quotient PDF BibTeX XML Cite \textit{L. Skula}, Math. Slovaca 58, No. 1, 5--10 (2008; Zbl 1164.11001) Full Text: DOI OpenURL References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.