On some congruences of sums of powers and Wolstenholme’s theorem for generalized harmonic numbers
摘要
In this paper, we first attempt to study sums of powers and to obtain some divisibility properties of the Stirling numbers of the first kind based on Newton-Girard’s identity. Then, using the obtained results, we study the divisibility properties of Wolstenholme’s theorem for the generalized harmonic numbers. Finally, we answer some open questions raised in 1992 by Y.Matiyasevich.