关于幂和的一些全等和广义调和数的沃斯滕霍姆定理

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-06-23 DOI:10.1007/s13226-024-00622-3

Morteza Bayat

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摘要

在本文中，我们首先尝试研究幂的和，并根据牛顿-吉拉德特性获得斯特林数第一类的一些可除性状。然后，利用所获得的结果，我们研究了广义谐波数的沃斯滕霍姆定理的可分性。最后，我们回答了马蒂亚舍维奇（Y.Matiyasevich）在 1992 年提出的一些未决问题。

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On some congruences of sums of powers and Wolstenholme’s theorem for generalized harmonic numbers

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.

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Indian Journal of Pure and Applied Mathematics

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