Congruences involving the reciprocals of central binomial coefficients

Abstract

We present several congruences modulo a power of prime $p$ concerning sums of the following type ${\sum }_{k=1}^{p-1}\frac{m^k}{k^r}{\left(\genfrac{}{}{0ex}{}{2k}{k}\right)}^{-1}$ which reveal some interesting connections with the analogous infinite series.

References in corpus (1)

• New harmonic number identities with applications

Cited by in corpus (2)

• Open Conjectures on Congruences
• New harmonic number identities with applications