{"title":"Two topics in number theory: the greatest k-free number that divides n and formulas for composite and prime numbers","authors":"R. Jakimczuk","doi":"10.56947/gjom.v14i1.1089","DOIUrl":null,"url":null,"abstract":"In the first part we study the greatest k-free number that divides n. Consequently, we generalize the kernel of the positive integer n. That is, the greatest square-free number that divides n. In the second part we obtain formulas for composite and prime numbers and prove some inequalities.","PeriodicalId":421614,"journal":{"name":"Gulf Journal of Mathematics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gulf Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56947/gjom.v14i1.1089","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 the first part we study the greatest k-free number that divides n. Consequently, we generalize the kernel of the positive integer n. That is, the greatest square-free number that divides n. In the second part we obtain formulas for composite and prime numbers and prove some inequalities.
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