{"title":"Remarks on the equation 1k + 2k + + (x − 1)k= xk","authors":"Jerzy Urbanowicz","doi":"10.1016/S1385-7258(88)80014-3","DOIUrl":null,"url":null,"abstract":"<div><p>For every <em>t</em> there is an explicitly given number <em>k</em><sub>0</sub> such that the equation 1<sup><em>k</em></sup> + 2<sup><em>k</em></sup> + + (x − 1)<sup><em>k</em></sup>= x<sup><em>k</em></sup> has no integer solutions <em>x</em>≥2 for all <em>k</em><sub>0</sub> for which the denominator of the <em>k</em>th Bernoulli number <em>B</em><sub>k</sub>has at most <em>t</em> distinct prime factors.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 343-348"},"PeriodicalIF":0.0000,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80014-3","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725888800143","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
For every t there is an explicitly given number k0 such that the equation 1k + 2k + + (x − 1)k= xk has no integer solutions x≥2 for all k0 for which the denominator of the kth Bernoulli number Bkhas at most t distinct prime factors.
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