{"title":"无平方 n 的 [nc] 形式的素数","authors":"S. I. Dimitrov","doi":"10.1007/s11253-024-02318-7","DOIUrl":null,"url":null,"abstract":"<p>Let [·] be the floor function. We show that if 1 <<i> c </i>< <span>\\(\\frac{3849}{3334}\\)</span><i>,</i> then there exist infinitely many prime numbers of the form [<i>n</i><sup><i>c</i></sup>]<i>,</i> where <i>n</i> is square free.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Primes of the form [nc] with Square-Free n\",\"authors\":\"S. I. Dimitrov\",\"doi\":\"10.1007/s11253-024-02318-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let [·] be the floor function. We show that if 1 <<i> c </i>< <span>\\\\(\\\\frac{3849}{3334}\\\\)</span><i>,</i> then there exist infinitely many prime numbers of the form [<i>n</i><sup><i>c</i></sup>]<i>,</i> where <i>n</i> is square free.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11253-024-02318-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11253-024-02318-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
让 [-] 成为底函数。我们证明，如果 1 < c < （\frac{3849}{3334}\），那么存在无穷多个形式为 [nc] 的素数，其中 n 是无平方数。
Let [·] be the floor function. We show that if 1 < c < \(\frac{3849}{3334}\), then there exist infinitely many prime numbers of the form [nc], where n is square free.
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