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

Year, pages: 2008, 5 - 10

In this note the sums $s(k,N)$ of reciprocals $∑_{((kp) / (N))< x <(((k+1)p) / (N))}\hspace{-6mm}((1) / (x)) \pmod p$ 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.

Skula, L. 2008. A note on some relations among special sums of reciprocals modulo $p^*$. In Mathematica Slovaca, vol. 58, no.1, pp. 5-10. 0139-9918.

Skula, L. (2008). A note on some relations among special sums of reciprocals modulo $p^*$. Mathematica Slovaca, 58(1), 5-10. 0139-9918.