{"title":"On some congruences of sums of powers and Wolstenholme’s theorem for generalized harmonic numbers","authors":"Morteza Bayat","doi":"10.1007/s13226-024-00622-3","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13226-024-00622-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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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