{"title":"对形式为\\(\\lfloor n^c\\rfloor\\), \\(\\lfloor n^c\\rfloor\\) +1的连续无立方数","authors":"Pinthira Tangsupphathawat, Teerapat Srichan","doi":"10.1007/s13370-025-01351-4","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider the existence of infinitely many consecutive cube-free numbers in Piatetski-Shapiro sequences. We prove that, for any fixed <span>\\(1<c<2\\)</span>, there exist infinitely many consecutive cube-free integers in Piatetski-Shapiro sequences.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 3","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On consecutive cube-free numbers of the form \\\\(\\\\lfloor n^c\\\\rfloor\\\\), \\\\(\\\\lfloor n^c\\\\rfloor\\\\)+1\",\"authors\":\"Pinthira Tangsupphathawat, Teerapat Srichan\",\"doi\":\"10.1007/s13370-025-01351-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we consider the existence of infinitely many consecutive cube-free numbers in Piatetski-Shapiro sequences. We prove that, for any fixed <span>\\\\(1<c<2\\\\)</span>, there exist infinitely many consecutive cube-free integers in Piatetski-Shapiro sequences.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"36 3\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-025-01351-4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-025-01351-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On consecutive cube-free numbers of the form \(\lfloor n^c\rfloor\), \(\lfloor n^c\rfloor\)+1
In this paper, we consider the existence of infinitely many consecutive cube-free numbers in Piatetski-Shapiro sequences. We prove that, for any fixed \(1<c<2\), there exist infinitely many consecutive cube-free integers in Piatetski-Shapiro sequences.
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